pulling in DFs and Merging (still needed?)

# #red wines
# Red_wine <- read.csv("wineQualityReds.csv", header=TRUE, sep = ",")
# Red_wine$Type <- 'Red'
# 
# #white wines
# White_wine <- read.csv("wineQualityWhites.csv", header=TRUE, sep = ",")
# White_wine$Type <- 'White'
# 
# ## consolidated
# Data <- rbind(Red_wine,White_wine)
# drops <- c("X")
# Data <- Data[ , !(names(Data) %in% drops)]
# Data
# 
# ##create final DF
# # write.csv(Data,"/Users/colinobrien/Desktop/repo/stats_6021/Stats_project_group_6/Data.csv", row.names = FALSE)
# # write.csv(Data,"/Users/colinobrien/Desktop/repo/stats_6021/Stats_project_group_6/Data", row.names = FALSE)
# ## both the Data and Data csv are the same. I know people prefer one format vs the other so I made both
library(tidyverse)
# library(ROCR)
library(faraway)
library(dplyr)
library(ggplot2)
library(reshape2)
library(leaps)
# install.packages("bestglm")
library(bestglm)
# install.packages("performance")
# library(performance)
knitr::opts_chunk$set(echo = TRUE)



## Load Datasets
full_wines_final <- read.csv("Data_Final.csv", header = TRUE, stringsAsFactors=TRUE)
# Drop quality for simplicity
full_wines_binary_with_qual<-full_wines_final
full_wines_binary <- subset(full_wines_final, select = -c(quality))
## Convert to 0 and 1 for readability
full_wines_binary$cat_quality <- as.integer(full_wines_binary$cat_quality == "High")

set.seed(90210) ##for reproducibility
sample<-sample.int(nrow(full_wines_binary), floor(.80*nrow(full_wines_binary)), replace = F)
train<-full_wines_binary[sample, ] ##training data frame
rownames(train) <- c(1:5197)
test<-full_wines_binary[-sample, ] ##test data frame

## Just for a single boxplot
train_with_qual<-full_wines_binary_with_qual[sample,]
test_with_qual<-full_wines_binary_with_qual[-sample,]


train

EDA

# drops_cats <- c("Type")
# No_cat_train <- train[ , !(names(train) %in% drops_cats)]
# # No_Type

pairs(train, lower.panel = NULL)

# Convert Type to binary to 0 and 1 for correlation
train$Type <- as.integer(train$Type == "White")
test$Type <- as.integer(test$Type == "White")
cor_train <- cor(train)
cor_train
                     fixed.acidity volatile.acidity   citric.acid
fixed.acidity           1.00000000       0.21475470  0.3281717780
volatile.acidity        0.21475470       1.00000000 -0.3756083338
citric.acid             0.32817178      -0.37560833  1.0000000000
residual.sugar         -0.11435784      -0.19711519  0.1413532761
chlorides               0.30907486       0.38572698  0.0368162603
free.sulfur.dioxide    -0.28545891      -0.36296634  0.1459151441
total.sulfur.dioxide   -0.32829667      -0.42380894  0.2063508767
density                 0.46102677       0.27340816  0.0934734894
pH                     -0.25053297       0.26430327 -0.3266522997
sulphates               0.31025439       0.23565770  0.0572809414
alcohol                -0.09179407      -0.03401873 -0.0006471143
Type                   -0.48713134      -0.65599571  0.1886904967
cat_quality            -0.07066799      -0.26538562  0.0778223488
                     residual.sugar   chlorides free.sulfur.dioxide
fixed.acidity           -0.11435784  0.30907486         -0.28545891
volatile.acidity        -0.19711519  0.38572698         -0.36296634
citric.acid              0.14135328  0.03681626          0.14591514
residual.sugar           1.00000000 -0.13267263          0.40674512
chlorides               -0.13267263  1.00000000         -0.20583891
free.sulfur.dioxide      0.40674512 -0.20583891          1.00000000
total.sulfur.dioxide     0.49459459 -0.29216595          0.71557904
density                  0.54686423  0.36564000          0.01712365
pH                      -0.26561668  0.04191555         -0.15788076
sulphates               -0.18182649  0.40162365         -0.19860411
alcohol                 -0.34842765 -0.25617404         -0.17708863
Type                     0.35126769 -0.52157700          0.48355395
cat_quality             -0.02120537 -0.18458731          0.04477089
                     total.sulfur.dioxide     density          pH
fixed.acidity                 -0.32829667  0.46102677 -0.25053297
volatile.acidity              -0.42380894  0.27340816  0.26430327
citric.acid                    0.20635088  0.09347349 -0.32665230
residual.sugar                 0.49459459  0.54686423 -0.26561668
chlorides                     -0.29216595  0.36564000  0.04191555
free.sulfur.dioxide            0.71557904  0.01712365 -0.15788076
total.sulfur.dioxide           1.00000000  0.02373810 -0.24648617
density                        0.02373810  1.00000000  0.01687243
pH                            -0.24648617  0.01687243  1.00000000
sulphates                     -0.27752789  0.27270901  0.18260830
alcohol                       -0.26082628 -0.67847127  0.11700658
Type                           0.70618430 -0.39538819 -0.33097301
cat_quality                   -0.04308093 -0.26437860  0.01854094
                       sulphates       alcohol        Type cat_quality
fixed.acidity         0.31025439 -0.0917940736 -0.48713134 -0.07066799
volatile.acidity      0.23565770 -0.0340187335 -0.65599571 -0.26538562
citric.acid           0.05728094 -0.0006471143  0.18869050  0.07782235
residual.sugar       -0.18182649 -0.3484276488  0.35126769 -0.02120537
chlorides             0.40162365 -0.2561740351 -0.52157700 -0.18458731
free.sulfur.dioxide  -0.19860411 -0.1770886318  0.48355395  0.04477089
total.sulfur.dioxide -0.27752789 -0.2608262814  0.70618430 -0.04308093
density               0.27270901 -0.6784712690 -0.39538819 -0.26437860
pH                    0.18260830  0.1170065815 -0.33097301  0.01854094
sulphates             1.00000000 -0.0136065691 -0.49215645  0.03195034
alcohol              -0.01360657  1.0000000000  0.03945167  0.39668183
Type                 -0.49215645  0.0394516700  1.00000000  0.12361294
cat_quality           0.03195034  0.3966818275  0.12361294  1.00000000
T_F_cor <- abs(cor_train)>.7
T_F_cor
                     fixed.acidity volatile.acidity citric.acid
fixed.acidity                 TRUE            FALSE       FALSE
volatile.acidity             FALSE             TRUE       FALSE
citric.acid                  FALSE            FALSE        TRUE
residual.sugar               FALSE            FALSE       FALSE
chlorides                    FALSE            FALSE       FALSE
free.sulfur.dioxide          FALSE            FALSE       FALSE
total.sulfur.dioxide         FALSE            FALSE       FALSE
density                      FALSE            FALSE       FALSE
pH                           FALSE            FALSE       FALSE
sulphates                    FALSE            FALSE       FALSE
alcohol                      FALSE            FALSE       FALSE
Type                         FALSE            FALSE       FALSE
cat_quality                  FALSE            FALSE       FALSE
                     residual.sugar chlorides free.sulfur.dioxide
fixed.acidity                 FALSE     FALSE               FALSE
volatile.acidity              FALSE     FALSE               FALSE
citric.acid                   FALSE     FALSE               FALSE
residual.sugar                 TRUE     FALSE               FALSE
chlorides                     FALSE      TRUE               FALSE
free.sulfur.dioxide           FALSE     FALSE                TRUE
total.sulfur.dioxide          FALSE     FALSE                TRUE
density                       FALSE     FALSE               FALSE
pH                            FALSE     FALSE               FALSE
sulphates                     FALSE     FALSE               FALSE
alcohol                       FALSE     FALSE               FALSE
Type                          FALSE     FALSE               FALSE
cat_quality                   FALSE     FALSE               FALSE
                     total.sulfur.dioxide density    pH sulphates alcohol
fixed.acidity                       FALSE   FALSE FALSE     FALSE   FALSE
volatile.acidity                    FALSE   FALSE FALSE     FALSE   FALSE
citric.acid                         FALSE   FALSE FALSE     FALSE   FALSE
residual.sugar                      FALSE   FALSE FALSE     FALSE   FALSE
chlorides                           FALSE   FALSE FALSE     FALSE   FALSE
free.sulfur.dioxide                  TRUE   FALSE FALSE     FALSE   FALSE
total.sulfur.dioxide                 TRUE   FALSE FALSE     FALSE   FALSE
density                             FALSE    TRUE FALSE     FALSE   FALSE
pH                                  FALSE   FALSE  TRUE     FALSE   FALSE
sulphates                           FALSE   FALSE FALSE      TRUE   FALSE
alcohol                             FALSE   FALSE FALSE     FALSE    TRUE
Type                                 TRUE   FALSE FALSE     FALSE   FALSE
cat_quality                         FALSE   FALSE FALSE     FALSE   FALSE
                      Type cat_quality
fixed.acidity        FALSE       FALSE
volatile.acidity     FALSE       FALSE
citric.acid          FALSE       FALSE
residual.sugar       FALSE       FALSE
chlorides            FALSE       FALSE
free.sulfur.dioxide  FALSE       FALSE
total.sulfur.dioxide  TRUE       FALSE
density              FALSE       FALSE
pH                   FALSE       FALSE
sulphates            FALSE       FALSE
alcohol              FALSE       FALSE
Type                  TRUE       FALSE
cat_quality          FALSE        TRUE
## create melted
melted_cor_train <- melt(cor_train)

##create heat map Consolidated
ggplot(data = melted_cor_train, aes(x=Var1, y=Var2, fill=value)) + 
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+ 
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Consolidated (Both Red and White)')

## creating red and white
train_White <- filter(train, Type == 1)
train_Red <- filter(train, Type == 0)


## droping red/white columns
train_White_NoType <- subset(train_White, select = -c(Type))
train_Red_NoType <- subset(train_Red, select = -c(Type))

## creating correlations
cor_train_White_NoType <- cor(train_White_NoType)
cor_train_Red_NoType <- cor(train_Red_NoType)

## melting
melted_cor_train_white <- melt(cor_train_White_NoType)
melted_cor_train_Red <- melt(cor_train_Red_NoType)

##ploting

##create heat map White
ggplot(data = melted_cor_train_white, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'White Wine')


##create heat map Red
ggplot(data = melted_cor_train_Red, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Red Wine')

ggplot(data = train, mapping = aes(x=Type)) + 
  geom_bar()

Regression Testing

## press formula (from class)
get_press <- function(model) {
  sum(((model$residuals)/ (1- (lm.influence(model)$hat)))^2)
}
## first go
full<-glm(cat_quality~., family=binomial, data=train)
summary(full)

Call:
glm(formula = cat_quality ~ ., family = binomial, data = train)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.4120  -0.8919   0.4303   0.8148   2.6198  

Coefficients:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)           1.102e+02  4.889e+01   2.253   0.0242 *  
fixed.acidity         7.676e-02  5.573e-02   1.377   0.1684    
volatile.acidity     -4.720e+00  3.291e-01 -14.342  < 2e-16 ***
citric.acid          -4.652e-01  2.875e-01  -1.618   0.1057    
residual.sugar        1.187e-01  2.104e-02   5.641 1.69e-08 ***
chlorides            -1.265e+00  1.195e+00  -1.059   0.2895    
free.sulfur.dioxide   1.345e-02  2.878e-03   4.672 2.98e-06 ***
total.sulfur.dioxide -5.753e-03  1.168e-03  -4.924 8.48e-07 ***
density              -1.211e+02  4.964e+01  -2.440   0.0147 *  
pH                    7.375e-01  3.316e-01   2.224   0.0261 *  
sulphates             2.096e+00  2.977e-01   7.042 1.89e-12 ***
alcohol               8.500e-01  6.635e-02  12.811  < 2e-16 ***
Type                 -5.562e-01  2.077e-01  -2.678   0.0074 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6833.2  on 5196  degrees of freedom
Residual deviance: 5335.5  on 5184  degrees of freedom
AIC: 5361.5

Number of Fisher Scoring iterations: 5
## removed all insignificant
reduced_1<-glm(formula = cat_quality~volatile.acidity+residual.sugar+free.sulfur.dioxide+total.sulfur.dioxide+density+pH+sulphates+alcohol+Type, family=binomial, data=train)
summary(reduced_1)

Call:
glm(formula = cat_quality ~ volatile.acidity + residual.sugar + 
    free.sulfur.dioxide + total.sulfur.dioxide + density + pH + 
    sulphates + alcohol + Type, family = binomial, data = train)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.3471  -0.9020   0.4275   0.8196   2.6625  

Coefficients:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)           76.416878  31.773373   2.405  0.01617 *  
volatile.acidity      -4.680054   0.305603 -15.314  < 2e-16 ***
residual.sugar         0.105875   0.014724   7.191 6.44e-13 ***
free.sulfur.dioxide    0.013183   0.002863   4.604 4.15e-06 ***
total.sulfur.dioxide  -0.005930   0.001162  -5.101 3.38e-07 ***
density              -86.733244  31.675484  -2.738  0.00618 ** 
pH                     0.595611   0.228953   2.601  0.00928 ** 
sulphates              1.930494   0.285976   6.751 1.47e-11 ***
alcohol                0.894713   0.051370  17.417  < 2e-16 ***
Type                  -0.523798   0.204855  -2.557  0.01056 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6833.2  on 5196  degrees of freedom
Residual deviance: 5341.5  on 5187  degrees of freedom
AIC: 5361.5

Number of Fisher Scoring iterations: 5
##evaluating model
Reduced1_AIC_train <- reduced_1$aic

##predicted quality for test data based on training data
preds<-predict(reduced_1,newdata=test, type="response")

reduced_1_error <- table(test$cat_quality, preds>0.5)

reduced_1_error
   
    FALSE TRUE
  0   240  236
  1   121  703
evulation_summary <- data.frame(
  attempt = 'reduced_1',
  AIC = Reduced1_AIC_train,
  PRESS = get_press(reduced_1),
  'False positive' = round(reduced_1_error[3]/(reduced_1_error[1]+reduced_1_error[3]),3),
  'False negative' = round(reduced_1_error[2]/(reduced_1_error[2]+reduced_1_error[4]),3),
  'Error Rate' = round((reduced_1_error[2]+reduced_1_error[3])/(reduced_1_error[1]+reduced_1_error[2]+reduced_1_error[3]+reduced_1_error[4]),3)
)
evulation_summary

second model

https://rstudio-pubs-static.s3.amazonaws.com/2897_9220b21cfc0c43a396ff9abf122bb351.html

# install.packages("bestglm")
## Prepare data
train.for.best.logistic <- within(train, {
    y <- cat_quality 
})

## Reorder variables
train.for.best.logistic <-
    train.for.best.logistic[, c("fixed.acidity","volatile.acidity","citric.acid","residual.sugar","total.sulfur.dioxide","density","chlorides","free.sulfur.dioxide",'pH','sulphates','alcohol','Type',"y")]

## Perform
res.best.logistic <-
    bestglm(Xy = train.for.best.logistic,
            family = binomial,          # binomial family for logistic
            IC = "AIC",                 # Information criteria for
            method = "exhaustive")
Morgan-Tatar search since family is non-gaussian.
res.best.logistic$BestModels
summary(res.best.logistic$BestModel)

Call:
glm(formula = y ~ ., family = family, data = Xi, weights = weights)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.4302  -0.8932   0.4282   0.8157   2.6350  

Coefficients:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)           1.147e+02  4.864e+01   2.358   0.0184 *  
fixed.acidity         8.518e-02  5.513e-02   1.545   0.1223    
volatile.acidity     -4.763e+00  3.268e-01 -14.574  < 2e-16 ***
citric.acid          -5.158e-01  2.834e-01  -1.820   0.0688 .  
residual.sugar        1.215e-01  2.085e-02   5.829 5.57e-09 ***
total.sulfur.dioxide -5.688e-03  1.167e-03  -4.876 1.08e-06 ***
density              -1.261e+02  4.936e+01  -2.554   0.0106 *  
free.sulfur.dioxide   1.332e-02  2.874e-03   4.633 3.61e-06 ***
pH                    8.012e-01  3.261e-01   2.457   0.0140 *  
sulphates             2.027e+00  2.897e-01   6.998 2.59e-12 ***
alcohol               8.553e-01  6.613e-02  12.934  < 2e-16 ***
Type                 -5.290e-01  2.059e-01  -2.569   0.0102 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6833.2  on 5196  degrees of freedom
Residual deviance: 5336.7  on 5185  degrees of freedom
AIC: 5360.7

Number of Fisher Scoring iterations: 5
reduced_4 <- res.best.logistic$BestModel
##evaluating model
Reduced4_AIC_train <- reduced_4$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4,newdata=test, type="response")

reduced_4_error <- table(test$cat_quality, preds>0.5)

evulation_summary_4 <- data.frame(
  attempt = 'reduced_4_error (all possible)',
  AIC = Reduced4_AIC_train,
  PRESS = get_press(reduced_4),
  'False positive' = round(reduced_4_error[3]/(reduced_4_error[1]+reduced_4_error[3]),3),
  'False negative' = round(reduced_4_error[2]/(reduced_4_error[2]+reduced_4_error[4]),3),
  'Error Rate' = round((reduced_4_error[2]+reduced_4_error[3])/(reduced_4_error[1]+reduced_4_error[2]+reduced_4_error[3]+reduced_4_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4)
# evulation_summary
# data.frame(check_collinearity(reduced_4))










#come back and add df stuff

in an effort to lower VIFs scores and correlation, I am removing fixed.acidity

reduced_4_2<-glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train)
summary(reduced_4_2)

Call:
glm(formula = cat_quality ~ volatile.acidity + citric.acid + 
    residual.sugar + total.sulfur.dioxide + density + free.sulfur.dioxide + 
    pH + sulphates + alcohol + Type, family = binomial, data = train)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.3469  -0.8997   0.4283   0.8144   2.6767  

Coefficients:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)           58.609496  33.904591   1.729   0.0839 .  
volatile.acidity      -4.841743   0.323737 -14.956  < 2e-16 ***
citric.acid           -0.434875   0.278458  -1.562   0.1184    
residual.sugar         0.099352   0.015302   6.493 8.43e-11 ***
total.sulfur.dioxide  -0.005815   0.001165  -4.993 5.94e-07 ***
density              -68.496442  33.901654  -2.020   0.0433 *  
free.sulfur.dioxide    0.013292   0.002871   4.630 3.66e-06 ***
pH                     0.465949   0.243355   1.915   0.0555 .  
sulphates              1.962718   0.287251   6.833 8.33e-12 ***
alcohol                0.918353   0.053777  17.077  < 2e-16 ***
Type                  -0.483884   0.206617  -2.342   0.0192 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6833.2  on 5196  degrees of freedom
Residual deviance: 5339.0  on 5186  degrees of freedom
AIC: 5361

Number of Fisher Scoring iterations: 5
##evaluating model
Reduced4_2_AIC_train <- reduced_4_2$aic
##predicted quality for test data based on training data
preds<-predict(reduced_4_2,newdata=test, type="response")
reduced_4_2_error <- table(test$cat_quality, preds>0.7)
#Curves
evulation_summary_4_2 <- data.frame(
  attempt = 'reduced_4_2_error (post VIF adjustments)',
  AIC = Reduced4_2_AIC_train,
  PRESS = get_press(reduced_4_2),
  'False positive' = round(reduced_4_2_error[3]/(reduced_4_2_error[1]+reduced_4_2_error[3]),3),
  'False negative' = round(reduced_4_2_error[2]/(reduced_4_2_error[2]+reduced_4_2_error[4]),3),
  'Error Rate' = round((reduced_4_2_error[2]+reduced_4_2_error[3])/(reduced_4_2_error[1]+reduced_4_2_error[2]+reduced_4_2_error[3]+reduced_4_2_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_2)
evulation_summary
NA
NA

now looking at outliers (with “best possible”)

summary(reduced_4)

Call:
glm(formula = y ~ ., family = family, data = Xi, weights = weights)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.4302  -0.8932   0.4282   0.8157   2.6350  

Coefficients:
                       Estimate Std. Error z value Pr(>|z|)    
(Intercept)           1.147e+02  4.864e+01   2.358   0.0184 *  
fixed.acidity         8.518e-02  5.513e-02   1.545   0.1223    
volatile.acidity     -4.763e+00  3.268e-01 -14.574  < 2e-16 ***
citric.acid          -5.158e-01  2.834e-01  -1.820   0.0688 .  
residual.sugar        1.215e-01  2.085e-02   5.829 5.57e-09 ***
total.sulfur.dioxide -5.688e-03  1.167e-03  -4.876 1.08e-06 ***
density              -1.261e+02  4.936e+01  -2.554   0.0106 *  
free.sulfur.dioxide   1.332e-02  2.874e-03   4.633 3.61e-06 ***
pH                    8.012e-01  3.261e-01   2.457   0.0140 *  
sulphates             2.027e+00  2.897e-01   6.998 2.59e-12 ***
alcohol               8.553e-01  6.613e-02  12.934  < 2e-16 ***
Type                 -5.290e-01  2.059e-01  -2.569   0.0102 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6833.2  on 5196  degrees of freedom
Residual deviance: 5336.7  on 5185  degrees of freedom
AIC: 5360.7

Number of Fisher Scoring iterations: 5

Now looking into outliers/influence

p <- 12
n <- 5197

Cooks

reduced_4_cook <-cooks.distance(reduced_4)
reduced_4_cook[reduced_4_cook>qf(0.5,p,n-p)]
named numeric(0)

DFFITs

##dffits
DFFITS<-dffits(reduced_4)
DDFFITS_influence <- DFFITS[abs(DFFITS)>2*sqrt(p/n)]
DDFFITS_influence
         83         115         133         148         149         171 
 0.11219627  0.10544184 -0.18411002 -0.09991644 -0.12785114 -0.11374142 
        183         202         206         225         249         292 
 0.10867107 -0.16045065 -0.11840913  0.10093853 -0.09841249  0.09816267 
        309         317         380         455         466         572 
 0.10078385  0.10471012 -0.11210579  0.09920619 -0.11390124  0.10171119 
        722         739         747         794         806         912 
-0.16019151  0.11513457  0.09736192 -0.10449640 -0.10120073  0.15167391 
        952         957        1010        1042        1055        1114 
 0.09704330 -0.16243046  0.11892944 -0.09863713 -0.11344570 -0.10497624 
       1139        1180        1241        1258        1270        1325 
 0.10300372 -0.18433803  0.10969510  0.09821539  0.10530848 -0.09678052 
       1347        1467        1493        1527        1528        1597 
-0.10103881  0.11642941 -0.11091048 -0.11561143 -0.12352731 -0.09863589 
       1620        1658        1693        1776        1846        1873 
-0.10722071 -0.09731307 -0.09795498 -0.10237941  0.12561590 -0.12529594 
       1882        1891        2002        2004        2020        2079 
-0.10642853  0.10446926  0.10894528  0.20125104  0.09637786 -0.10426201 
       2103        2148        2203        2256        2258        2285 
 0.09853506 -0.27921127 -0.10129823 -0.10012511  0.10312207  0.10896369 
       2305        2350        2353        2361        2383        2410 
 0.13774801  0.09853162 -0.15221240 -0.11012001 -0.10852123 -0.12636270 
       2434        2461        2465        2487        2494        2497 
 0.12603788 -0.15438799 -0.10048416  0.10125735 -0.12151311  0.10319545 
       2521        2525        2527        2551        2594        2650 
-0.10237941 -0.10131647 -0.10242317 -0.09669244 -0.10722071 -0.10178224 
       2696        2699        2772        2781        2801        2840 
-0.11840913 -0.10221624  0.20008361 -0.10703304 -0.11210579  0.16042062 
       2852        2892        2948        2965        2978        2994 
-0.10974330  0.09732574 -0.09841249 -0.09647583 -0.11806742  0.14196649 
       2995        2997        3018        3030        3041        3051 
 0.09920619 -0.13745390  0.10099437 -0.14516539  0.16695970 -0.12151311 
       3065        3079        3126        3155        3188        3274 
-0.21978199  0.10160629  0.17165718  0.13048253  0.17504970 -0.10882370 
       3282        3330        3347        3367        3378        3381 
 0.10171119  0.09880694 -0.11538312 -0.11374142 -0.10444247  0.10177520 
       3496        3526        3557        3564        3571        3709 
 0.12512066 -0.15993715 -0.13072803 -0.13765634 -0.11317090 -0.11344570 
       3721        3740        3752        3809        3823        3843 
-0.15438799 -0.10404207 -0.15579966 -0.10786452  0.88209659  0.10113003 
       3848        3895        3922        4024        4035        4065 
 0.11006220 -0.18174866 -0.12028121 -0.10640867 -0.11091048  0.09637786 
       4071        4112        4125        4131        4132        4140 
-0.31948427 -0.12024521 -0.10057784 -0.10147570  0.17165718 -0.11174867 
       4260        4300        4401        4425        4463        4490 
-0.11267738  0.10499625 -0.10880237 -0.10594437 -0.12634536 -0.09991644 
       4512        4547        4610        4627        4678        4687 
-0.09647583 -0.17220454  0.10741187 -0.21859387 -0.10392610  0.12149435 
       4783        4790        4794        4829        4873        5045 
 0.12315874  0.10969510 -0.09878535 -0.11104591 -0.16746164 -0.10529190 
       5091        5178        5187 
-0.10703304  0.11264144  0.10894528 

DFBETAs

DFBETAS<-dfbetas(reduced_4)
abs(DFBETAS)>2/sqrt(n)
     (Intercept) fixed.acidity volatile.acidity citric.acid residual.sugar
1          FALSE         FALSE            FALSE       FALSE          FALSE
2          FALSE         FALSE            FALSE       FALSE          FALSE
3          FALSE          TRUE            FALSE        TRUE           TRUE
4          FALSE         FALSE            FALSE       FALSE          FALSE
5          FALSE         FALSE            FALSE       FALSE          FALSE
6          FALSE         FALSE            FALSE       FALSE          FALSE
7          FALSE         FALSE            FALSE       FALSE          FALSE
8          FALSE         FALSE            FALSE       FALSE           TRUE
9          FALSE         FALSE            FALSE       FALSE          FALSE
10          TRUE          TRUE            FALSE        TRUE           TRUE
11         FALSE         FALSE            FALSE       FALSE          FALSE
12         FALSE         FALSE            FALSE       FALSE          FALSE
13         FALSE         FALSE            FALSE       FALSE          FALSE
14         FALSE         FALSE            FALSE       FALSE          FALSE
15         FALSE         FALSE            FALSE       FALSE          FALSE
16         FALSE         FALSE            FALSE       FALSE          FALSE
17         FALSE         FALSE            FALSE       FALSE          FALSE
18         FALSE         FALSE            FALSE       FALSE          FALSE
19         FALSE         FALSE            FALSE       FALSE          FALSE
20         FALSE         FALSE            FALSE       FALSE          FALSE
21         FALSE         FALSE            FALSE        TRUE          FALSE
22         FALSE         FALSE            FALSE       FALSE          FALSE
23         FALSE          TRUE            FALSE       FALSE           TRUE
24         FALSE         FALSE            FALSE       FALSE          FALSE
25         FALSE          TRUE             TRUE       FALSE          FALSE
26         FALSE         FALSE            FALSE       FALSE          FALSE
27         FALSE         FALSE            FALSE       FALSE          FALSE
28         FALSE         FALSE            FALSE       FALSE          FALSE
29         FALSE         FALSE            FALSE       FALSE          FALSE
30         FALSE         FALSE            FALSE       FALSE          FALSE
31         FALSE         FALSE            FALSE       FALSE          FALSE
32         FALSE         FALSE            FALSE       FALSE          FALSE
33         FALSE         FALSE            FALSE       FALSE          FALSE
34         FALSE         FALSE            FALSE       FALSE          FALSE
35         FALSE         FALSE            FALSE       FALSE          FALSE
36         FALSE         FALSE            FALSE       FALSE          FALSE
37         FALSE         FALSE            FALSE       FALSE          FALSE
38         FALSE         FALSE            FALSE       FALSE          FALSE
39         FALSE         FALSE            FALSE       FALSE          FALSE
40         FALSE         FALSE            FALSE       FALSE          FALSE
41         FALSE         FALSE             TRUE       FALSE          FALSE
42         FALSE         FALSE            FALSE       FALSE          FALSE
43         FALSE         FALSE            FALSE       FALSE          FALSE
44         FALSE         FALSE            FALSE       FALSE          FALSE
45         FALSE         FALSE            FALSE       FALSE          FALSE
46         FALSE         FALSE            FALSE       FALSE          FALSE
47         FALSE         FALSE            FALSE       FALSE           TRUE
48         FALSE         FALSE            FALSE        TRUE          FALSE
49         FALSE         FALSE            FALSE       FALSE          FALSE
50         FALSE         FALSE            FALSE       FALSE          FALSE
51         FALSE         FALSE            FALSE       FALSE          FALSE
52         FALSE         FALSE            FALSE       FALSE          FALSE
53         FALSE         FALSE            FALSE       FALSE          FALSE
54         FALSE         FALSE            FALSE       FALSE          FALSE
55         FALSE         FALSE            FALSE       FALSE          FALSE
56         FALSE         FALSE            FALSE       FALSE          FALSE
57         FALSE         FALSE            FALSE       FALSE          FALSE
58         FALSE         FALSE            FALSE       FALSE          FALSE
59         FALSE         FALSE             TRUE        TRUE          FALSE
60         FALSE         FALSE            FALSE       FALSE          FALSE
61         FALSE         FALSE            FALSE       FALSE          FALSE
62         FALSE         FALSE            FALSE       FALSE          FALSE
63         FALSE         FALSE            FALSE       FALSE          FALSE
64         FALSE         FALSE            FALSE       FALSE          FALSE
65          TRUE          TRUE            FALSE       FALSE           TRUE
66         FALSE         FALSE            FALSE       FALSE          FALSE
67         FALSE         FALSE            FALSE       FALSE          FALSE
68         FALSE         FALSE            FALSE       FALSE          FALSE
69         FALSE         FALSE            FALSE       FALSE          FALSE
70         FALSE         FALSE            FALSE       FALSE          FALSE
71         FALSE         FALSE            FALSE       FALSE          FALSE
72         FALSE         FALSE            FALSE       FALSE          FALSE
73         FALSE         FALSE            FALSE       FALSE          FALSE
74         FALSE         FALSE            FALSE       FALSE          FALSE
75         FALSE         FALSE            FALSE       FALSE          FALSE
76         FALSE         FALSE            FALSE       FALSE          FALSE
77         FALSE         FALSE            FALSE       FALSE          FALSE
78         FALSE         FALSE            FALSE       FALSE          FALSE
79         FALSE         FALSE            FALSE       FALSE          FALSE
80         FALSE         FALSE            FALSE       FALSE          FALSE
81         FALSE          TRUE            FALSE       FALSE          FALSE
82         FALSE         FALSE            FALSE       FALSE          FALSE
83         FALSE          TRUE             TRUE        TRUE          FALSE
     total.sulfur.dioxide density free.sulfur.dioxide    pH sulphates
1                   FALSE   FALSE               FALSE FALSE     FALSE
2                   FALSE   FALSE               FALSE FALSE     FALSE
3                   FALSE   FALSE               FALSE  TRUE     FALSE
4                   FALSE   FALSE               FALSE FALSE     FALSE
5                   FALSE   FALSE               FALSE FALSE     FALSE
6                   FALSE   FALSE               FALSE FALSE     FALSE
7                   FALSE   FALSE               FALSE FALSE     FALSE
8                   FALSE   FALSE                TRUE FALSE      TRUE
9                   FALSE   FALSE               FALSE FALSE     FALSE
10                   TRUE    TRUE                TRUE FALSE     FALSE
11                  FALSE   FALSE               FALSE FALSE     FALSE
12                  FALSE   FALSE               FALSE FALSE     FALSE
13                  FALSE   FALSE               FALSE FALSE     FALSE
14                  FALSE   FALSE               FALSE FALSE     FALSE
15                  FALSE   FALSE               FALSE FALSE      TRUE
16                  FALSE   FALSE               FALSE FALSE     FALSE
17                  FALSE   FALSE               FALSE FALSE      TRUE
18                  FALSE   FALSE               FALSE  TRUE     FALSE
19                  FALSE   FALSE               FALSE FALSE     FALSE
20                  FALSE   FALSE               FALSE FALSE     FALSE
21                  FALSE   FALSE               FALSE FALSE     FALSE
22                  FALSE   FALSE               FALSE FALSE     FALSE
23                  FALSE   FALSE               FALSE FALSE     FALSE
24                  FALSE   FALSE               FALSE FALSE     FALSE
25                  FALSE   FALSE               FALSE FALSE     FALSE
26                  FALSE   FALSE               FALSE FALSE     FALSE
27                  FALSE   FALSE               FALSE FALSE     FALSE
28                  FALSE   FALSE               FALSE FALSE     FALSE
29                  FALSE   FALSE               FALSE FALSE     FALSE
30                  FALSE   FALSE               FALSE FALSE     FALSE
31                  FALSE   FALSE               FALSE FALSE     FALSE
32                  FALSE   FALSE               FALSE FALSE     FALSE
33                  FALSE   FALSE               FALSE FALSE     FALSE
34                  FALSE   FALSE               FALSE FALSE     FALSE
35                  FALSE   FALSE               FALSE FALSE     FALSE
36                  FALSE   FALSE               FALSE FALSE     FALSE
37                  FALSE   FALSE               FALSE FALSE     FALSE
38                  FALSE   FALSE               FALSE FALSE     FALSE
39                  FALSE   FALSE               FALSE FALSE     FALSE
40                  FALSE   FALSE               FALSE FALSE     FALSE
41                  FALSE   FALSE               FALSE FALSE      TRUE
42                  FALSE   FALSE               FALSE FALSE     FALSE
43                  FALSE   FALSE                TRUE FALSE      TRUE
44                  FALSE   FALSE               FALSE FALSE     FALSE
45                  FALSE   FALSE               FALSE FALSE     FALSE
46                  FALSE   FALSE               FALSE FALSE     FALSE
47                  FALSE   FALSE               FALSE  TRUE     FALSE
48                  FALSE   FALSE               FALSE FALSE     FALSE
49                  FALSE   FALSE               FALSE FALSE     FALSE
50                  FALSE   FALSE               FALSE FALSE     FALSE
51                  FALSE   FALSE               FALSE FALSE     FALSE
52                  FALSE   FALSE               FALSE FALSE     FALSE
53                  FALSE   FALSE               FALSE FALSE     FALSE
54                  FALSE   FALSE               FALSE FALSE     FALSE
55                  FALSE   FALSE               FALSE FALSE     FALSE
56                  FALSE   FALSE               FALSE FALSE     FALSE
57                  FALSE   FALSE               FALSE FALSE     FALSE
58                  FALSE   FALSE               FALSE FALSE     FALSE
59                  FALSE   FALSE               FALSE FALSE     FALSE
60                  FALSE   FALSE               FALSE FALSE     FALSE
61                  FALSE   FALSE               FALSE  TRUE     FALSE
62                  FALSE   FALSE               FALSE FALSE     FALSE
63                  FALSE   FALSE               FALSE FALSE     FALSE
64                  FALSE   FALSE               FALSE FALSE     FALSE
65                  FALSE    TRUE               FALSE  TRUE     FALSE
66                  FALSE   FALSE               FALSE FALSE     FALSE
67                  FALSE   FALSE               FALSE FALSE     FALSE
68                  FALSE   FALSE               FALSE FALSE     FALSE
69                  FALSE   FALSE               FALSE FALSE     FALSE
70                  FALSE   FALSE                TRUE FALSE     FALSE
71                  FALSE   FALSE               FALSE FALSE     FALSE
72                  FALSE   FALSE               FALSE FALSE     FALSE
73                  FALSE   FALSE               FALSE FALSE     FALSE
74                  FALSE   FALSE               FALSE FALSE     FALSE
75                  FALSE   FALSE               FALSE FALSE     FALSE
76                  FALSE   FALSE               FALSE FALSE     FALSE
77                  FALSE   FALSE               FALSE FALSE     FALSE
78                  FALSE   FALSE               FALSE FALSE     FALSE
79                  FALSE   FALSE               FALSE FALSE     FALSE
80                  FALSE   FALSE               FALSE FALSE     FALSE
81                  FALSE   FALSE               FALSE  TRUE     FALSE
82                  FALSE   FALSE               FALSE FALSE     FALSE
83                  FALSE   FALSE               FALSE  TRUE     FALSE
     alcohol  Type
1      FALSE FALSE
2      FALSE FALSE
3      FALSE FALSE
4      FALSE FALSE
5      FALSE FALSE
6      FALSE  TRUE
7      FALSE FALSE
8      FALSE FALSE
9      FALSE FALSE
10      TRUE  TRUE
11     FALSE FALSE
12     FALSE FALSE
13     FALSE FALSE
14     FALSE FALSE
15     FALSE FALSE
16     FALSE FALSE
17     FALSE FALSE
18     FALSE FALSE
19     FALSE FALSE
20     FALSE FALSE
21     FALSE FALSE
22     FALSE FALSE
23     FALSE FALSE
24     FALSE FALSE
25     FALSE FALSE
26     FALSE FALSE
27     FALSE FALSE
28     FALSE FALSE
29     FALSE FALSE
30     FALSE FALSE
31     FALSE FALSE
32     FALSE FALSE
33     FALSE FALSE
34     FALSE FALSE
35     FALSE FALSE
36     FALSE FALSE
37     FALSE FALSE
38     FALSE FALSE
39     FALSE FALSE
40     FALSE FALSE
41     FALSE  TRUE
42     FALSE FALSE
43     FALSE FALSE
44     FALSE FALSE
45     FALSE FALSE
46     FALSE FALSE
47     FALSE FALSE
48     FALSE FALSE
49     FALSE FALSE
50     FALSE FALSE
51     FALSE FALSE
52     FALSE FALSE
53     FALSE FALSE
54     FALSE FALSE
55     FALSE FALSE
56     FALSE FALSE
57     FALSE FALSE
58     FALSE FALSE
59     FALSE  TRUE
60     FALSE FALSE
61     FALSE FALSE
62     FALSE FALSE
63     FALSE FALSE
64     FALSE FALSE
65      TRUE FALSE
66     FALSE FALSE
67     FALSE FALSE
68     FALSE FALSE
69     FALSE FALSE
70     FALSE FALSE
71     FALSE FALSE
72     FALSE FALSE
73     FALSE FALSE
74     FALSE FALSE
75     FALSE FALSE
76     FALSE FALSE
77     FALSE FALSE
78     FALSE FALSE
79     FALSE FALSE
80     FALSE FALSE
81     FALSE FALSE
82     FALSE FALSE
83     FALSE  TRUE
 [ reached getOption("max.print") -- omitted 5114 rows ]

leverage

##leverages
lev<-lm.influence(reduced_4)$hat
##identify high leverage points
leverages <- lev[lev>2*p/n]
leverages
         25          48          53          65         133         145 
0.004849640 0.007980011 0.007028687 0.005763404 0.022975591 0.005173793 
        171         175         187         202         225         228 
0.005219474 0.004875721 0.006161515 0.005447858 0.006756723 0.005384983 
        248         249         255         282         299         309 
0.008357256 0.004801962 0.005867337 0.005674515 0.005484537 0.010250038 
        332         333         339         345         361         380 
0.004754212 0.004686940 0.004990699 0.005924282 0.006389325 0.006435227 
        383         417         427         455         466         489 
0.006875256 0.004943798 0.004867913 0.009165489 0.006894948 0.007172970 
        516         557         600         607         708         722 
0.010652503 0.005554653 0.005521417 0.005900775 0.004918820 0.005283197 
        730         747         749         765         770         806 
0.005147385 0.005767084 0.005739296 0.005627857 0.004853531 0.005540805 
        828         873         899         912         945         957 
0.007828147 0.006995196 0.005410461 0.009841709 0.005463074 0.011974020 
        965         995        1010        1037        1055        1114 
0.005623028 0.014123202 0.004921736 0.006212390 0.006141910 0.005265677 
       1132        1139        1140        1152        1169        1176 
0.006966068 0.005959266 0.006430522 0.006059376 0.004777701 0.005844926 
       1180        1188        1241        1255        1265        1300 
0.012489770 0.004953075 0.004856461 0.004777701 0.005672314 0.006081786 
       1304        1306        1325        1345        1375        1427 
0.005100154 0.005735362 0.005574241 0.004711974 0.006383030 0.004930082 
       1467        1479        1481        1482        1493        1495 
0.006002690 0.006720302 0.005242150 0.014123202 0.007969759 0.004698112 
       1507        1518        1527        1528        1612        1614 
0.004854829 0.005124711 0.005382525 0.005299431 0.009822894 0.008993399 
       1638        1642        1649        1667        1711        1719 
0.007179770 0.007952008 0.005823824 0.007088896 0.004814463 0.004889259 
       1768        1801        1829        1845        1846        1873 
0.004851478 0.004848096 0.004766974 0.006026022 0.005410441 0.005408285 
       1882        1887        1891        1894        1929        1933 
0.004657424 0.005524176 0.005158734 0.004960904 0.007033838 0.006340479 
       1935        1941        1956        1979        2002        2004 
0.005367322 0.005155488 0.004781888 0.006023785 0.005565063 0.013293498 
       2019        2097        2106        2120        2135        2137 
0.005674515 0.004945639 0.005391888 0.005466349 0.006032961 0.005458302 
       2144        2148        2155        2165        2177        2203 
0.005593131 0.020382883 0.005008204 0.005477897 0.005419422 0.004636068 
       2211        2218        2232        2270        2281        2294 
0.004669295 0.019421769 0.006338349 0.007220018 0.006915245 0.006786840 
       2305        2306        2317        2350        2353        2361 
0.010603689 0.005150988 0.011839638 0.004828941 0.012864370 0.005000134 
       2371        2379        2383        2391        2396        2400 
0.005408758 0.005477511 0.006524792 0.005514256 0.008839432 0.007088896 
       2410        2420        2434        2461        2469        2494 
0.007468644 0.004680633 0.020272029 0.016139547 0.005146048 0.008984307 
       2497        2525        2602        2623        2650        2663 
0.006080078 0.006378263 0.007252053 0.006726745 0.005745347 0.006470764 
       2680        2688        2699        2772        2777        2779 
0.007158112 0.005672314 0.007016065 0.013464526 0.012846622 0.006384951 
       2798        2801        2812        2840        2849        2852 
0.004748024 0.006435227 0.007487716 0.008115731 0.006556965 0.004882351 
       2856        2900        2910        2912        2946        2948 
0.006384951 0.005156491 0.006091693 0.004787344 0.005054188 0.004801962 
       2965        2969        2971        2990        2994        2995 
0.005054630 0.005674515 0.004891501 0.005016018 0.005494005 0.009165489 
       3004        3008        3012        3018        3021        3030 
0.004821646 0.005616506 0.005184523 0.007585533 0.007383966 0.008916163 
       3041        3046        3051        3052        3065        3074 
0.016455429 0.005893423 0.008984307 0.005310204 0.012183875 0.004946746 
       3126        3130        3155        3188        3221        3274 
0.019492710 0.005384397 0.007093095 0.015836977 0.005940855 0.005995139 
       3292        3309        3324        3332        3347        3367 
0.004646160 0.005018396 0.005633797 0.008055287 0.007555507 0.005219474 
       3378        3381        3413        3418        3419        3446 
0.005844088 0.007215437 0.007952008 0.004995318 0.005468012 0.004726109 
       3469        3474        3487        3496        3519        3524 
0.005565027 0.004674916 0.005068929 0.009369520 0.005543214 0.004635661 
       3526        3545        3549        3557        3587        3611 
0.013422322 0.004757291 0.004918820 0.007684917 0.004872856 0.004872856 
       3622        3650        3666        3709        3710        3720 
0.004733307 0.005857163 0.006405776 0.006141910 0.005615658 0.006389325 
       3721        3727        3741        3752        3763        3769 
0.016139547 0.006618658 0.004870547 0.016330934 0.005287558 0.004728145 
       3787        3792        3807        3818        3820        3823 
0.004943798 0.007689718 0.005998108 0.010775791 0.007366569 0.323058874 
       3824        3835        3843        3848        3854        3863 
0.012258040 0.004967080 0.005005760 0.006333501 0.007689718 0.008161154 
       3890        3895        3912        3917        3922        3953 
0.005616506 0.019354101 0.004912963 0.007690767 0.010025916 0.019421769 
       3991        4024        4035        4071        4088        4112 
0.004912256 0.005151978 0.007969759 0.033246417 0.004918863 0.007559978 
       4125        4129        4131        4132        4140        4143 
0.005498808 0.004805200 0.007131721 0.019492710 0.009613280 0.004686940 
       4174        4180        4191        4195        4260        4287 
0.006136951 0.005524176 0.005514261 0.005146048 0.009759507 0.004801486 
       4300        4301        4343        4362        4401        4463 
0.005225384 0.005310204 0.007165155 0.005507166 0.005566348 0.017712588 
       4482        4493        4511        4512        4547        4553 
0.008767404 0.007154999 0.006995196 0.005054630 0.009347506 0.010326676 
       4558        4585        4627        4633        4639        4687 
0.006875101 0.004851478 0.014885235 0.005546699 0.004777701 0.006998472 
       4693        4696        4710        4715        4754        4759 
0.004640983 0.005081857 0.005440630 0.005196371 0.006386644 0.007418423 
       4790        4829        4873        4902        4908        4972 
0.004856461 0.006130203 0.012769233 0.005893423 0.008892413 0.004912256 
       4992        5040        5041        5054        5087        5107 
0.006275606 0.004889259 0.007383966 0.006838011 0.004875721 0.006541276 
       5154        5178        5187 
0.007677790 0.006034090 0.005565063 

outlier

reduced_4.res <- reduced_4$residuals
crit<-qt(1-0.05/(2*n), n-p-1)
outliers <- reduced_4.res[abs(reduced_4.res)>crit]
outliers
          8          12          21          30          83          85 
  -5.913799 -112.810937   -5.131140  -28.388375    7.064053   -4.902421 
         86         101         115         122         142         148 
   5.268800   -6.738462    5.835978  -11.281066   -4.900743   -5.950818 
        149         154         166         183         202         206 
  -8.284466   -4.614577    5.536043   18.759111  -11.064846   -6.976696 
        218         245         264         281         288         372 
   7.906909   -7.166119    6.562536    4.514517   -9.756502   -9.170360 
        373         440         505         509         525         548 
  -4.811386   -4.829656   10.431685   -5.199469   32.192103  -42.498339 
        566         589         629         655         657         659 
  10.705696   -4.616565   -5.057653    4.903313  -10.049213   -4.454203 
        675         687         701         706         717         721 
  -5.471326   -6.529182   -9.150344   -8.992792   -7.819105   -8.206050 
        722         725         739         751         768         774 
 -11.839559   -6.756563    4.469453    9.211716   -5.691134   -4.977692 
        788         794         795         817         819         833 
   5.293240   -5.395176   -9.673765  -13.711257   -4.723057  -10.325351 
        840         844         875         888         902         903 
  -4.977692    7.896471  -13.765446    4.511825   -4.486556    4.815690 
        917         954         964         967         991        1039 
  -9.997107   11.645455   -5.057653    7.233862   -4.851860  -29.863426 
       1077        1081        1107        1124        1133        1156 
  -6.559467   -5.979445  -11.538933   -9.743607   -8.597773 -358.992053 
       1162        1167        1171        1172        1226        1235 
  -5.913799  -13.370172   -5.991466  -13.904782  -24.686598  -22.516690 
       1257        1258        1263        1270        1305        1318 
   9.644487    4.622980    6.011786    8.044160   -5.145541   -5.100743 
       1344        1356        1387        1412        1428        1436 
   5.658642   -6.254700   -4.851860   -9.750690  -11.498443   -8.316040 
       1487        1497        1510        1524        1610        1620 
   7.687631    5.004046   -7.060659    4.482981  -16.343618   -5.238351 
       1652        1658        1665        1669        1693        1706 
 -11.418067   -7.852930   -5.163340  -16.484320   -4.689106   -4.877840 
       1776        1787        1790        1840        1930        1951 
 -16.318931   -5.613721    9.189242   -4.798258   -6.274087   -7.515991 
       1958        1998        2004        2006        2018        2040 
  -6.682392    9.251057    4.599440    5.240035    7.500553    4.734365 
       2041        2059        2079        2115        2119        2148 
  -5.264313  -15.336442   -6.043512  -23.388238   -4.859254   -6.605338 
       2156        2167        2195        2205        2220        2256 
  -5.287846   -9.600193   -5.857549   -4.579628    4.948918   -9.053372 
       2258        2262        2284        2290        2313        2329 
  17.356606   -7.264594  -16.484320    5.684278   -4.851860   -7.041619 
       2334        2335        2337        2386        2439        2452 
  -7.417245   -4.555771   -5.816303  -12.954904    9.264406   -8.282663 
       2480        2485        2506        2521        2536        2579 
  -4.793832  -18.780311    4.541019  -16.318931   -4.884719    9.211716 
       2594        2628        2629        2642        2660        2661 
  -5.238351   -6.381604    4.489202   -5.096416    4.453651   -5.461202 
       2666        2696        2702        2718        2727        2735 
  -6.254700   -6.976696    7.233862   -6.726264    5.198906   -6.197960 
       2745        2763        2772        2781        2793        2795 
  -6.606402  -11.892705    4.431016   -8.362063   -4.697738   -4.530220 
       2802        2840        2866        2892        2898        2955 
  -7.010108    4.976958   -7.349414   11.007314   -4.528817  -14.101843 
       2978        2994        2997        3005        3025        3040 
 -13.426497    6.463923  -14.095802    5.659028   -4.737794   -8.881971 
       3042        3065        3072        3079        3090        3105 
  -6.738462   -7.313679   -6.423514   16.073667    5.085934   -5.548543 
       3133        3149        3196        3210        3243        3248 
  -5.466040   -5.426271   -6.355608   -7.747739   -6.033627    5.580542 
       3257        3264        3322        3336        3343        3351 
  -4.595999   -5.857549   -9.308640    9.264406   -4.501913    5.867902 
       3362        3369        3400        3410        3414        3424 
 -13.219174  -12.293034   -4.896657   -5.318501   -9.993826   -6.001601 
       3434        3461        3522        3564        3566        3571 
 -10.863890   -6.353654   -8.866347   -8.604661   -6.119343   -6.889088 
       3582        3605        3629        3638        3711        3716 
  -5.322449   -9.260519   -8.348111   -6.028213   -6.506898    5.779253 
       3740        3750        3784        3816        3841        3853 
  -7.586267    5.060560   -4.746179   -6.432015   -6.569981    5.240035 
       3855        3866        3903        3910        3913        3915 
 -10.826648   -4.935304    5.739331   -9.056519   -4.882192  -16.323382 
       3942        3947        3951        4003        4019        4090 
  -5.403135   -4.485039   -6.092031   -8.881971   -4.877840   -4.542401 
       4093        4111        4116        4127        4144        4145 
  -5.913799  -15.362967   -5.909070   -7.854482    4.541019   -8.716350 
       4151        4156        4159        4170        4233        4243 
  -9.593344   -7.055209  -42.578664   -4.837952   -4.614577   -5.850980 
       4248        4306        4311        4329        4354        4356 
 -14.114484   -5.627580    4.678171  -11.261020  -14.672621   -5.417642 
       4460        4490        4503        4505        4527        4544 
   6.046933   -5.950818   -6.716718    4.453651    4.477563   -8.992792 
       4547        4556        4580        4610        4614        4627 
  -4.960846   -4.813642  -13.243536    5.353589   -5.833289   -4.965536 
       4650        4656        4659        4677        4701        4713 
  -4.896657    4.644296   -6.288973    5.012168  -10.498461    8.507914 
       4729        4783        4794        4815        4858        4880 
  -6.726264    7.580155   -5.470226   -5.334876   -5.096416   -6.738462 
       4887        4910        4924        4939        4988        5045 
   5.612130   -6.821823   -4.543092    4.488823   -6.821823  -11.196377 
       5049        5051        5091        5095        5133        5140 
  -4.972743   -6.197392   -8.362063   -7.809710   -5.399943    4.815690 
       5179        5195 
  -8.541941  -10.162346 
## outliers removed
outliers_index <- attr(outliers, "names")
outliers_index <- as.numeric(outliers_index)
train_no_outliers <- train[-(outliers_index),]

#leverages removed
lererages_index <- attr(leverages, "names")
lererages_index <- as.numeric(lererages_index)
train_no_leverages <- train[-(lererages_index),]

# DDFFITS_influence
DDFFITS_index <- attr(DDFFITS_influence, "names")
DDFFITS_index <- as.numeric(DDFFITS_index)
train_no_DDFFITS <- train[-(DDFFITS_index),]

# all "non-normal" removed
all_special <- c(DDFFITS_index,lererages_index,outliers_index)
train_nothing_special <- train[-(all_special),]
train_nothing_special
NA
NA
NA
NA
vif(train[c(2,3,4,7,8,6,9,10,11)])
    volatile.acidity          citric.acid       residual.sugar 
            1.818602             1.505238             3.353752 
total.sulfur.dioxide              density  free.sulfur.dioxide 
            2.850601             5.664883             2.099196 
                  pH            sulphates              alcohol 
            1.338240             1.427424             2.890129 
train_temp<-train
# as.factor(train_temp$Type)<-numeric(train_temp$Type)
#train_temp
# as.factor

train_temp$Type <- as.numeric(train_temp$Type)-1
train_temp$Type <- as.integer(train_temp$Type)
train_temp

creating reduced

reduced_4_3 <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_no_outliers)

reduced_4_4_lev <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_no_leverages)

reduced_4_5_DDFFITS <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_no_DDFFITS)

reduced_4_6_no_special <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_nothing_special)
# summary(reduced_4_6_no_special)
## checking colinearity / VIF scores
# reduced_4_3_col <- data.frame('reduced_4_3' = check_collinearity(reduced_4_3))
# reduced_4_3_col_VIF <- reduced_4_3_col[c('reduced_4_3.Term','reduced_4_3.VIF')]
# reduced_4_3_col_VIF
# 
# reduced_4_4_lev_col <- data.frame('reduced_4_4_lev' = check_collinearity(reduced_4_4_lev))
# reduced_4_4_lev_col_VIF <- reduced_4_4_lev_col[c('reduced_4_4_lev.Term','reduced_4_4_lev.VIF')]
# reduced_4_4_lev_col_VIF
# 
# 
# reduced_4_5_DDFFITS_col <- data.frame('reduced_4_5_DDFFITS' = check_collinearity(reduced_4_5_DDFFITS))
# reduced_4_5_DDFFITS_col_VIF <- reduced_4_5_DDFFITS_col[c('reduced_4_5_DDFFITS.Term','reduced_4_5_DDFFITS.VIF')]
# reduced_4_5_DDFFITS_col_VIF
# 
# reduced_4_6_no_special_col <- data.frame('reduced_4_6_no_special' = check_collinearity(reduced_4_6_no_special))
# reduced_4_6_no_special_col_VIF <- reduced_4_6_no_special_col[c('reduced_4_6_no_special.Term','reduced_4_6_no_special.VIF')]
# reduced_4_6_no_special_col_VIF
# 
# VIF_summary <- data.frame('0'=reduced_4_3_col_VIF['reduced_4_3.Term'],
#                           '1'=reduced_4_3_col_VIF['reduced_4_3.VIF'],
#                           '2'=reduced_4_4_lev_col_VIF['reduced_4_4_lev.VIF'],
#                           '3'=reduced_4_5_DDFFITS_col_VIF['reduced_4_5_DDFFITS.VIF'],
#                           '4'=reduced_4_6_no_special_col_VIF['reduced_4_6_no_special.VIF'])
# colnames(VIF_summary) <- c('Predictor Variable','4_3.VIF.Outliers','4_4_lev.VIF','4_5_DDFFITS.VIF','4_6_no_special.VIF')
# VIF_summary

## VIF for Outliers
### cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type


#
reg_4_VIF_test <- vif(train_temp[c(1,2,3,4,7,8,6,9,10,11,12)])
reg_4_2_VIF_test <- vif(train_temp[c(2,3,4,7,8,6,9,10,11,12)])
outliers_VIF <- vif(train_no_outliers[c(2,3,4,7,8,6,9,10,11,12)])
leverage_VIF <- vif(train_no_leverages[c(2,3,4,7,8,6,9,10,11,12)])
DDFFITS_VIF <- vif(train_no_DDFFITS[c(2,3,4,7,8,6,9,10,11,12)])
nothing_special <- vif(train_nothing_special[c(2,3,4,7,8,6,9,10,11,12)])


reg_4_VIF_test
       fixed.acidity     volatile.acidity          citric.acid       residual.sugar total.sulfur.dioxide 
            4.962487             2.139008             1.585795             9.280982             3.974170 
             density  free.sulfur.dioxide                   pH            sulphates              alcohol 
           21.338984             2.189173             2.483275             1.514014             5.371286 
                Type 
            7.045601 
VIF_summary_test <- data.frame('best_possible_VIF (post)'=reg_4_2_VIF_test,
                               'outliers_VIF'=outliers_VIF,
                               'leverage_VIF'=leverage_VIF,
                               'DDFFITS_VIF'= DDFFITS_VIF,
                               'nothing_special'=nothing_special)
VIF_summary_test
NA
##evaluating model
Reduced4_3_AIC_train <- reduced_4_3$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_3,newdata=test, type="response")

reduced_4_3_error <- table(test$cat_quality, preds>0.6)

evulation_summary_4_3 <- data.frame(
  attempt = 'reduced_4_3_error_outliers',
  AIC = Reduced4_3_AIC_train,
  PRESS = get_press(reduced_4_3),
  'False positive' = round(reduced_4_3_error[3]/(reduced_4_3_error[1]+reduced_4_3_error[3]),3),
  'False negative' = round(reduced_4_3_error[2]/(reduced_4_3_error[2]+reduced_4_3_error[4]),3),
  'Error Rate' = round((reduced_4_3_error[2]+reduced_4_3_error[3])/(reduced_4_3_error[1]+reduced_4_3_error[2]+reduced_4_3_error[3]+reduced_4_3_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_3)
evulation_summary
##evaluating model leverage
reduced_4_4_lev_AIC_train <- reduced_4_4_lev$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_4_lev,newdata=test, type="response")

reduced_4_4_lev_error <- table(test$cat_quality, preds>0.65)

evulation_summary_4_4_lev <- data.frame(
  attempt = 'reduced_4_4_lev_error',
  AIC = reduced_4_4_lev_AIC_train,
  PRESS = get_press(reduced_4_4_lev),
  'False positive' = round(reduced_4_4_lev_error[3]/(reduced_4_4_lev_error[1]+reduced_4_4_lev_error[3]),3),
  'False negative' = round(reduced_4_4_lev_error[2]/(reduced_4_4_lev_error[2]+reduced_4_4_lev_error[4]),3),
  'Error Rate' = round((reduced_4_4_lev_error[2]+reduced_4_4_lev_error[3])/(reduced_4_4_lev_error[1]+reduced_4_4_lev_error[2]+reduced_4_4_lev_error[3]+reduced_4_4_lev_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_4_lev)
evulation_summary
##evaluating model DDFFITS
reduced_4_5_DDFFITS_AIC_train <- reduced_4_5_DDFFITS$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_5_DDFFITS,newdata=test, type="response")

reduced_4_5_DDFFITS_error <- table(test$cat_quality, preds>0.7)

evulation_summary_4_5_DDFFITS <- data.frame(
  attempt = 'reduced_4_5_DDFFITS_error',
  AIC = reduced_4_5_DDFFITS_AIC_train,
  PRESS = get_press(reduced_4_5_DDFFITS),
  'False positive' = round(reduced_4_5_DDFFITS_error[3]/(reduced_4_5_DDFFITS_error[1]+reduced_4_5_DDFFITS_error[3]),3),
  'False negative' = round(reduced_4_5_DDFFITS_error[2]/(reduced_4_5_DDFFITS_error[2]+reduced_4_5_DDFFITS_error[4]),3),
  'Error Rate' = round((reduced_4_5_DDFFITS_error[2]+reduced_4_5_DDFFITS_error[3])/(reduced_4_5_DDFFITS_error[1]+reduced_4_5_DDFFITS_error[2]+reduced_4_5_DDFFITS_error[3]+reduced_4_5_DDFFITS_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_5_DDFFITS)
evulation_summary
##evaluating model DDFFITS
reduced_4_6_no_special_AIC_train <- reduced_4_6_no_special$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_6_no_special,newdata=test, type="response")

reduced_4_6_no_special_error <- table(test$cat_quality, preds>0.8)

evulation_summary_4_6_no_special <- data.frame(
  attempt = 'reduced_4_6_no_special_error',
  AIC = reduced_4_6_no_special_AIC_train,
  PRESS = get_press(reduced_4_6_no_special),
  'False positive' = round(reduced_4_6_no_special_error[3]/(reduced_4_6_no_special_error[1]+reduced_4_6_no_special_error[3]),3),
  'False negative' = round(reduced_4_6_no_special_error[2]/(reduced_4_6_no_special_error[2]+reduced_4_6_no_special_error[4]),3),
  'Error Rate' = round((reduced_4_6_no_special_error[2]+reduced_4_6_no_special_error[3])/(reduced_4_6_no_special_error[1]+reduced_4_6_no_special_error[2]+reduced_4_6_no_special_error[3]+reduced_4_6_no_special_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_6_no_special)
evulation_summary

ROC Curves and AUC

## reduced_1
# detach(package:performance, unload=TRUE)
## FYI the performance package causes ROC curves to not work
library(ROCR)



# reduced_1
preds<-predict(reduced_1,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_1")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
reduced_1_auc <- auc@y.values

## reduced_4
preds<-predict(reduced_4,newdata=test, type="response")
rates4<-prediction(preds, test$cat_quality)
roc_result<-performance(rates4,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4")
lines(x = c(0,1), y = c(0,1), col="red")


auc4<-performance(rates4, measure = "auc")
reduced_4_auc <- auc4@y.values

## reduced_4_2
preds<-predict(reduced_4_2,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_2")
lines(x = c(0,1), y = c(0,1), col="red")


auc4_2<-performance(rates, measure = "auc")
reduced_4_2_auc <- auc4_2@y.values

## reduced_4_3
preds<-predict(reduced_4_3,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_3")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
reduced_4_3_auc <- auc@y.values

## reduced_4_4_lev 
preds<-predict(reduced_4_4_lev,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_4_lev")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
reduced_4_4_lev_auc <- auc@y.values

## reduced_4_5_DDFFITS 
preds<-predict(reduced_4_5_DDFFITS,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_5_DDFFITS")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
reduced_4_5_DDFFITS_auc <- auc@y.values

## reduced_4_6_no_special 
preds<-predict(reduced_4_6_no_special,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_6_no_special")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
reduced_4_6_no_special_auc <- auc@y.values

AUC_summary <- data.frame('reduced_1'=reduced_1_auc,
                          'reduced_4'=reduced_4_auc,
                          'reduced_4_2'=reduced_4_2_auc,
                          'reduced_4_3'=reduced_4_3_auc,
                          'reduced_4_4_lev'=reduced_4_4_lev_auc,
                          'reduced_4_5_DDFFITS'=reduced_4_5_DDFFITS_auc,
                          'reduced_4_6_no_special'=reduced_4_6_no_special_auc)
colnames(AUC_summary) <- c('reduced_1','reduced_4','reduced_4_2','reduced_4_3','reduced_4_4_lev','reduced_4_5_DDFFITS','reduced_4_6_no_special')

AUC_summary

Ryan’s part starts here

The goal is to make 3 models: One for just white, one for just red, and one with interaction terms with the type of wine.

After that, the models will be trained on the filtered datasets and the resulting scores will be added to the evaluation summary.

Red wine only model

regfull_Red<-glm(cat_quality~., family="binomial", data=train_Red_NoType)
regnull_Red<-glm(cat_quality~1, family="binomial", data=train_Red_NoType)
step(regnull_Red, scope=list(lower=regnull_Red, upper=regfull_Red), direction="forward")
Start:  AIC=1811.89
cat_quality ~ 1

                       Df Deviance    AIC
+ alcohol               1   1540.6 1544.6
+ volatile.acidity      1   1680.6 1684.6
+ total.sulfur.dioxide  1   1726.9 1730.9
+ sulphates             1   1741.1 1745.1
+ citric.acid           1   1778.7 1782.7
+ density               1   1780.0 1784.0
+ chlorides             1   1795.4 1799.4
+ fixed.acidity         1   1797.8 1801.8
+ free.sulfur.dioxide   1   1803.8 1807.8
<none>                      1809.9 1811.9
+ pH                    1   1809.8 1813.8
+ residual.sugar        1   1809.9 1813.9

Step:  AIC=1544.61
cat_quality ~ alcohol

                       Df Deviance    AIC
+ volatile.acidity      1   1450.7 1456.7
+ sulphates             1   1492.7 1498.7
+ total.sulfur.dioxide  1   1507.4 1513.4
+ fixed.acidity         1   1521.6 1527.6
+ citric.acid           1   1523.5 1529.5
+ pH                    1   1528.7 1534.7
+ density               1   1535.8 1541.8
<none>                      1540.6 1544.6
+ free.sulfur.dioxide   1   1539.2 1545.2
+ residual.sugar        1   1539.8 1545.8
+ chlorides             1   1540.5 1546.5

Step:  AIC=1456.66
cat_quality ~ alcohol + volatile.acidity

                       Df Deviance    AIC
+ total.sulfur.dioxide  1   1417.1 1425.1
+ sulphates             1   1427.5 1435.5
+ fixed.acidity         1   1448.1 1456.1
+ free.sulfur.dioxide   1   1448.1 1456.1
<none>                      1450.7 1456.7
+ citric.acid           1   1449.0 1457.0
+ density               1   1449.5 1457.5
+ residual.sugar        1   1449.8 1457.8
+ pH                    1   1449.9 1457.9
+ chlorides             1   1450.7 1458.7

Step:  AIC=1425.14
cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide

                      Df Deviance    AIC
+ sulphates            1   1387.4 1397.4
+ free.sulfur.dioxide  1   1409.8 1419.8
<none>                     1417.1 1425.1
+ pH                   1   1415.8 1425.8
+ density              1   1416.1 1426.1
+ fixed.acidity        1   1416.2 1426.2
+ citric.acid          1   1416.8 1426.8
+ residual.sugar       1   1417.0 1427.0
+ chlorides            1   1417.1 1427.1

Step:  AIC=1397.37
cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide + 
    sulphates

                      Df Deviance    AIC
+ free.sulfur.dioxide  1   1379.6 1391.6
+ chlorides            1   1380.0 1392.0
+ citric.acid          1   1383.9 1395.9
<none>                     1387.4 1397.4
+ residual.sugar       1   1387.1 1399.1
+ fixed.acidity        1   1387.3 1399.3
+ pH                   1   1387.4 1399.4
+ density              1   1387.4 1399.4

Step:  AIC=1391.64
cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide + 
    sulphates + free.sulfur.dioxide

                 Df Deviance    AIC
+ chlorides       1   1372.6 1386.6
<none>                1379.6 1391.6
+ citric.acid     1   1377.9 1391.9
+ pH              1   1379.3 1393.3
+ fixed.acidity   1   1379.3 1393.3
+ residual.sugar  1   1379.5 1393.5
+ density         1   1379.6 1393.6

Step:  AIC=1386.63
cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide + 
    sulphates + free.sulfur.dioxide + chlorides

                 Df Deviance    AIC
<none>                1372.6 1386.6
+ pH              1   1371.2 1387.2
+ citric.acid     1   1372.1 1388.1
+ fixed.acidity   1   1372.2 1388.2
+ residual.sugar  1   1372.2 1388.2
+ density         1   1372.6 1388.6

Call:  glm(formula = cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide + 
    sulphates + free.sulfur.dioxide + chlorides, family = "binomial", 
    data = train_Red_NoType)

Coefficients:
         (Intercept)               alcohol      volatile.acidity  
            -8.02155               0.85512              -2.93115  
total.sulfur.dioxide             sulphates   free.sulfur.dioxide  
            -0.01843               2.63739               0.02326  
           chlorides  
            -4.10141  

Degrees of Freedom: 1308 Total (i.e. Null);  1302 Residual
Null Deviance:      1810 
Residual Deviance: 1373     AIC: 1387

The model looks great after the foward selection! Time to test and add to the evaluation summary.

model1_Red<-glm(formula = cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide + 
    sulphates + free.sulfur.dioxide + chlorides, family = "binomial", 
    data = train_Red_NoType)

summary(model1_Red)

Call:
glm(formula = cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide + 
    sulphates + free.sulfur.dioxide + chlorides, family = "binomial", 
    data = train_Red_NoType)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.0655  -0.8628   0.3239   0.8474   2.3082  

Coefficients:
                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)          -8.021553   0.886912  -9.044  < 2e-16 ***
alcohol               0.855123   0.078409  10.906  < 2e-16 ***
volatile.acidity     -2.931148   0.413395  -7.090 1.34e-12 ***
total.sulfur.dioxide -0.018428   0.002926  -6.297 3.03e-10 ***
sulphates             2.637391   0.456973   5.771 7.86e-09 ***
free.sulfur.dioxide   0.023257   0.008608   2.702  0.00689 ** 
chlorides            -4.101411   1.588464  -2.582  0.00982 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1809.9  on 1308  degrees of freedom
Residual deviance: 1372.6  on 1302  degrees of freedom
AIC: 1386.6

Number of Fisher Scoring iterations: 4

##evaluating model
model1_Red_AIC_train <- model1_Red$aic
##predicted quality for test data based on training data
test_Red_NoType<-subset(test, Type == 0, select=-c(Type))
preds<-predict(model1_Red,newdata=test_Red_NoType, type="response")
model1_Red_error <- table(test_Red_NoType$cat_quality, preds>0.7)
#Curves
evulation_summary_1R <- data.frame(
  attempt = 'model1_Red',
  AIC = model1_Red_AIC_train,
  PRESS = get_press(model1_Red),
  'False positive' = round(model1_Red_error[3]/(model1_Red_error[1]+model1_Red_error[3]),3),
  'False negative' = round(model1_Red_error[2]/(model1_Red_error[2]+model1_Red_error[4]),3),
  'Error Rate' = round((model1_Red_error[2]+model1_Red_error[3])/(model1_Red_error[1]+model1_Red_error[2]+model1_Red_error[3]+model1_Red_error[4]),3)
)

compare_models<-rbind(evulation_summary[1,],evulation_summary_1R)
compare_models

evulation_summary <- rbind(evulation_summary,evulation_summary_1R)
evulation_summary
NA
# model1_Red
library(ROCR)
preds<-predict(model1_Red,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_Red")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
model1_Red_auc <- auc@y.values

White wine only model

regfull_White<-glm(cat_quality~., family="binomial", data=train_White_NoType)
regnull_White<-glm(cat_quality~1,family="binomial", data=train_White_NoType)
step(regnull_White, scope=list(lower=regnull_White, upper=regfull_White), direction="forward")
Start:  AIC=4947.36
cat_quality ~ 1

                       Df Deviance    AIC
+ alcohol               1   4280.3 4284.3
+ density               1   4668.2 4672.2
+ volatile.acidity      1   4758.7 4762.7
+ chlorides             1   4805.4 4809.4
+ total.sulfur.dioxide  1   4831.9 4835.9
+ fixed.acidity         1   4912.0 4916.0
+ pH                    1   4914.3 4918.3
+ residual.sugar        1   4919.1 4923.1
+ sulphates             1   4934.7 4938.7
<none>                      4945.4 4947.4
+ free.sulfur.dioxide   1   4945.2 4949.2
+ citric.acid           1   4945.4 4949.4

Step:  AIC=4284.29
cat_quality ~ alcohol

                       Df Deviance    AIC
+ volatile.acidity      1   4030.1 4036.1
+ residual.sugar        1   4214.8 4220.8
+ free.sulfur.dioxide   1   4235.1 4241.1
+ density               1   4253.7 4259.7
+ sulphates             1   4261.3 4267.3
+ fixed.acidity         1   4267.3 4273.3
+ chlorides             1   4273.1 4279.1
+ pH                    1   4276.2 4282.2
+ citric.acid           1   4276.3 4282.3
<none>                      4280.3 4284.3
+ total.sulfur.dioxide  1   4279.4 4285.4

Step:  AIC=4036.1
cat_quality ~ alcohol + volatile.acidity

                       Df Deviance    AIC
+ residual.sugar        1   3942.1 3950.1
+ density               1   3984.6 3992.6
+ free.sulfur.dioxide   1   3999.3 4007.3
+ sulphates             1   4013.2 4021.2
+ fixed.acidity         1   4014.8 4022.8
+ total.sulfur.dioxide  1   4020.2 4028.2
<none>                      4030.1 4036.1
+ pH                    1   4028.3 4036.3
+ chlorides             1   4028.6 4036.6
+ citric.acid           1   4030.1 4038.1

Step:  AIC=3950.11
cat_quality ~ alcohol + volatile.acidity + residual.sugar

                       Df Deviance    AIC
+ fixed.acidity         1   3923.0 3933.0
+ sulphates             1   3924.2 3934.2
+ free.sulfur.dioxide   1   3930.2 3940.2
+ density               1   3932.9 3942.9
+ pH                    1   3934.3 3944.3
<none>                      3942.1 3950.1
+ total.sulfur.dioxide  1   3941.1 3951.1
+ citric.acid           1   3941.6 3951.6
+ chlorides             1   3942.1 3952.1

Step:  AIC=3932.95
cat_quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity

                       Df Deviance    AIC
+ sulphates             1   3904.7 3916.7
+ free.sulfur.dioxide   1   3914.0 3926.0
<none>                      3923.0 3933.0
+ pH                    1   3921.5 3933.5
+ total.sulfur.dioxide  1   3921.7 3933.7
+ density               1   3921.9 3933.9
+ citric.acid           1   3922.7 3934.7
+ chlorides             1   3923.0 3935.0

Step:  AIC=3916.74
cat_quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + 
    sulphates

                       Df Deviance    AIC
+ free.sulfur.dioxide   1   3896.9 3910.9
+ density               1   3898.2 3912.2
<none>                      3904.7 3916.7
+ pH                    1   3904.6 3918.6
+ total.sulfur.dioxide  1   3904.6 3918.6
+ citric.acid           1   3904.7 3918.7
+ chlorides             1   3904.7 3918.7

Step:  AIC=3910.91
cat_quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + 
    sulphates + free.sulfur.dioxide

                       Df Deviance    AIC
+ density               1   3890.7 3906.7
+ total.sulfur.dioxide  1   3894.7 3910.7
<none>                      3896.9 3910.9
+ pH                    1   3896.8 3912.8
+ chlorides             1   3896.9 3912.9
+ citric.acid           1   3896.9 3912.9

Step:  AIC=3906.7
cat_quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + 
    sulphates + free.sulfur.dioxide + density

                       Df Deviance    AIC
+ pH                    1   3885.2 3903.2
<none>                      3890.7 3906.7
+ total.sulfur.dioxide  1   3889.6 3907.6
+ chlorides             1   3890.7 3908.7
+ citric.acid           1   3890.7 3908.7

Step:  AIC=3903.24
cat_quality ~ alcohol + volatile.acidity + residual.sugar + fixed.acidity + 
    sulphates + free.sulfur.dioxide + density + pH

                       Df Deviance    AIC
<none>                      3885.2 3903.2
+ total.sulfur.dioxide  1   3884.3 3904.3
+ chlorides             1   3885.0 3905.0
+ citric.acid           1   3885.1 3905.1

Call:  glm(formula = cat_quality ~ alcohol + volatile.acidity + residual.sugar + 
    fixed.acidity + sulphates + free.sulfur.dioxide + density + 
    pH, family = "binomial", data = train_White_NoType)

Coefficients:
        (Intercept)              alcohol     volatile.acidity  
          2.041e+02            8.487e-01           -6.416e+00  
     residual.sugar        fixed.acidity            sulphates  
          1.563e-01           -9.407e-03            1.877e+00  
free.sulfur.dioxide              density                   pH  
          6.778e-03           -2.165e+02            8.920e-01  

Degrees of Freedom: 3887 Total (i.e. Null);  3879 Residual
Null Deviance:      4945 
Residual Deviance: 3885     AIC: 3903

The model looks good after the foward selection, but the predictor fixed.acidity can be removed. The density VIF is above ten, but jsut barely. For now, it will be left in. Time to test and add to the evaluation summary.

model1_White<-glm(formula = cat_quality ~ alcohol + volatile.acidity + residual.sugar + 
    fixed.acidity + sulphates + free.sulfur.dioxide + density + 
    pH, family = "binomial", data = train_White_NoType)


summary(model1_White)

Call:
glm(formula = cat_quality ~ alcohol + volatile.acidity + residual.sugar + 
    fixed.acidity + sulphates + free.sulfur.dioxide + density + 
    pH, family = "binomial", data = train_White_NoType)

Deviance Residuals: 
   Min      1Q  Median      3Q     Max  
-3.198  -0.888   0.437   0.798   2.507  

Coefficients:
                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)          2.041e+02  6.993e+01   2.918  0.00352 ** 
alcohol              8.487e-01  9.686e-02   8.763  < 2e-16 ***
volatile.acidity    -6.416e+00  4.477e-01 -14.329  < 2e-16 ***
residual.sugar       1.563e-01  2.746e-02   5.689 1.27e-08 ***
fixed.acidity       -9.407e-03  7.582e-02  -0.124  0.90126    
sulphates            1.877e+00  4.028e-01   4.661 3.15e-06 ***
free.sulfur.dioxide  6.778e-03  2.540e-03   2.669  0.00761 ** 
density             -2.165e+02  7.088e+01  -3.054  0.00226 ** 
pH                   8.920e-01  3.886e-01   2.295  0.02172 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 4945.4  on 3887  degrees of freedom
Residual deviance: 3885.2  on 3879  degrees of freedom
AIC: 3903.2

Number of Fisher Scoring iterations: 5
model1_White<-glm(formula = cat_quality ~ alcohol + volatile.acidity + residual.sugar + sulphates + free.sulfur.dioxide + density + 
    pH, family = "binomial", data = train_White_NoType)

summary(model1_White)

Call:
glm(formula = cat_quality ~ alcohol + volatile.acidity + residual.sugar + 
    sulphates + free.sulfur.dioxide + density + pH, family = "binomial", 
    data = train_White_NoType)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.1956  -0.8867   0.4377   0.7961   2.5070  

Coefficients:
                      Estimate Std. Error z value Pr(>|z|)    
(Intercept)          2.105e+02  4.762e+01   4.420 9.87e-06 ***
alcohol              8.408e-01  7.311e-02  11.501  < 2e-16 ***
volatile.acidity    -6.407e+00  4.417e-01 -14.504  < 2e-16 ***
residual.sugar       1.586e-01  1.972e-02   8.045 8.66e-16 ***
sulphates            1.885e+00  3.978e-01   4.739 2.14e-06 ***
free.sulfur.dioxide  6.796e-03  2.536e-03   2.680  0.00737 ** 
density             -2.230e+02  4.773e+01  -4.673 2.97e-06 ***
pH                   9.247e-01  2.859e-01   3.235  0.00122 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 4945.4  on 3887  degrees of freedom
Residual deviance: 3885.3  on 3880  degrees of freedom
AIC: 3901.3

Number of Fisher Scoring iterations: 5

##evaluating model
model1_White_AIC_train <- model1_White$aic
##predicted quality for test data based on training data
test_White_NoType<-subset(test, Type == 1, select=-c(Type))
preds<-predict(model1_White,newdata=test_White_NoType, type="response")
model1_White_error <- table(test_White_NoType$cat_quality, preds>0.7)
#Curves
evulation_summary_1W <- data.frame(
  attempt = 'model1_White',
  AIC = model1_White_AIC_train,
  PRESS = get_press(model1_White),
  'False positive' = round(model1_White_error[3]/(model1_White_error[1]+model1_White_error[3]),3),
  'False negative' = round(model1_White_error[2]/(model1_White_error[2]+model1_White_error[4]),3),
  'Error Rate' = round((model1_White_error[2]+model1_White_error[3])/(model1_White_error[1]+model1_White_error[2]+model1_White_error[3]+model1_White_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_1W)
evulation_summary


compare_models<-rbind(compare_models,evulation_summary_1W)
compare_models
NA

The model with interaction terms

regfull_int<-glm(cat_quality~.*Type, family="binomial", data=train)
regnull_int<-glm(cat_quality~1,family="binomial", data=train)
step(regnull_int, scope=list(lower=regnull_int, upper=regfull_int), direction="forward")
Start:  AIC=6835.15
cat_quality ~ 1

                       Df Deviance    AIC
+ alcohol               1   5904.3 5908.3
+ density               1   6450.6 6454.6
+ volatile.acidity      1   6468.6 6472.6
+ chlorides             1   6640.0 6644.0
+ Type                  1   6755.3 6759.3
+ citric.acid           1   6801.3 6805.3
+ fixed.acidity         1   6807.6 6811.6
+ free.sulfur.dioxide   1   6822.7 6826.7
+ total.sulfur.dioxide  1   6823.5 6827.5
+ sulphates             1   6827.8 6831.8
+ residual.sugar        1   6830.8 6834.8
<none>                      6833.2 6835.2
+ pH                    1   6831.4 6835.4

Step:  AIC=5908.3
cat_quality ~ alcohol

                       Df Deviance    AIC
+ volatile.acidity      1   5539.7 5545.7
+ residual.sugar        1   5781.4 5787.4
+ free.sulfur.dioxide   1   5810.8 5816.8
+ Type                  1   5826.6 5832.6
+ chlorides             1   5861.3 5867.3
+ citric.acid           1   5864.8 5870.8
+ total.sulfur.dioxide  1   5872.3 5878.3
+ fixed.acidity         1   5893.0 5899.0
+ pH                    1   5895.5 5901.5
+ sulphates             1   5897.6 5903.6
<none>                      5904.3 5908.3
+ density               1   5903.5 5909.5

Step:  AIC=5545.67
cat_quality ~ alcohol + volatile.acidity

                       Df Deviance    AIC
+ density               1   5476.5 5484.5
+ sulphates             1   5477.1 5485.1
+ residual.sugar        1   5500.5 5508.5
+ Type                  1   5504.4 5512.4
+ total.sulfur.dioxide  1   5524.4 5532.4
+ pH                    1   5532.9 5540.9
+ free.sulfur.dioxide   1   5533.7 5541.7
<none>                      5539.7 5545.7
+ chlorides             1   5537.8 5545.8
+ citric.acid           1   5537.9 5545.9
+ fixed.acidity         1   5538.6 5546.6

Step:  AIC=5484.51
cat_quality ~ alcohol + volatile.acidity + density

                       Df Deviance    AIC
+ sulphates             1   5442.1 5452.1
+ citric.acid           1   5463.1 5473.1
+ fixed.acidity         1   5463.8 5473.8
+ total.sulfur.dioxide  1   5464.0 5474.0
+ Type                  1   5465.2 5475.2
+ pH                    1   5471.0 5481.0
+ free.sulfur.dioxide   1   5471.2 5481.2
+ residual.sugar        1   5472.8 5482.8
<none>                      5476.5 5484.5
+ chlorides             1   5476.3 5486.3

Step:  AIC=5452.14
cat_quality ~ alcohol + volatile.acidity + density + sulphates

                       Df Deviance    AIC
+ residual.sugar        1   5419.3 5431.3
+ fixed.acidity         1   5422.1 5434.1
+ citric.acid           1   5424.1 5436.1
+ free.sulfur.dioxide   1   5432.7 5444.7
+ total.sulfur.dioxide  1   5435.6 5447.6
+ pH                    1   5439.3 5451.3
+ chlorides             1   5439.4 5451.4
<none>                      5442.1 5452.1
+ Type                  1   5440.5 5452.5

Step:  AIC=5431.3
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar

                       Df Deviance    AIC
+ Type                  1   5379.2 5393.2
+ total.sulfur.dioxide  1   5385.9 5399.9
+ citric.acid           1   5404.8 5418.8
+ pH                    1   5410.7 5424.7
+ fixed.acidity         1   5415.4 5429.4
<none>                      5419.3 5431.3
+ free.sulfur.dioxide   1   5417.5 5431.5
+ chlorides             1   5418.8 5432.8

Step:  AIC=5393.24
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type

                        Df Deviance    AIC
+ volatile.acidity:Type  1   5348.7 5364.7
+ total.sulfur.dioxide   1   5371.4 5387.4
+ pH                     1   5371.9 5387.9
+ citric.acid            1   5372.7 5388.7
+ free.sulfur.dioxide    1   5373.9 5389.9
+ residual.sugar:Type    1   5374.6 5390.6
+ chlorides              1   5376.4 5392.4
+ density:Type           1   5377.1 5393.1
<none>                       5379.2 5393.2
+ fixed.acidity          1   5378.4 5394.4
+ alcohol:Type           1   5379.2 5395.2
+ sulphates:Type         1   5379.2 5395.2

Step:  AIC=5364.67
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + volatile.acidity:Type

                       Df Deviance    AIC
+ total.sulfur.dioxide  1   5342.0 5360.0
+ residual.sugar:Type   1   5343.3 5361.3
+ free.sulfur.dioxide   1   5344.5 5362.5
+ pH                    1   5344.7 5362.7
+ density:Type          1   5345.2 5363.2
+ chlorides             1   5345.8 5363.8
+ citric.acid           1   5346.2 5364.2
<none>                      5348.7 5364.7
+ alcohol:Type          1   5348.3 5366.3
+ sulphates:Type        1   5348.5 5366.5
+ fixed.acidity         1   5348.6 5366.6

Step:  AIC=5359.98
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + volatile.acidity:Type

                            Df Deviance    AIC
+ total.sulfur.dioxide:Type  1   5303.1 5323.1
+ free.sulfur.dioxide        1   5323.1 5343.1
+ residual.sugar:Type        1   5337.0 5357.0
+ pH                         1   5337.3 5357.3
+ chlorides                  1   5338.9 5358.9
+ density:Type               1   5339.4 5359.4
+ citric.acid                1   5339.9 5359.9
<none>                           5342.0 5360.0
+ alcohol:Type               1   5341.7 5361.7
+ fixed.acidity              1   5341.8 5361.8
+ sulphates:Type             1   5341.9 5361.9

Step:  AIC=5323.07
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + volatile.acidity:Type + 
    Type:total.sulfur.dioxide

                      Df Deviance    AIC
+ free.sulfur.dioxide  1   5286.9 5308.9
+ density:Type         1   5295.6 5317.6
+ pH                   1   5299.6 5321.6
+ alcohol:Type         1   5300.2 5322.2
+ chlorides            1   5300.3 5322.3
<none>                     5303.1 5323.1
+ citric.acid          1   5302.1 5324.1
+ sulphates:Type       1   5302.2 5324.2
+ residual.sugar:Type  1   5302.4 5324.4
+ fixed.acidity        1   5302.9 5324.9

Step:  AIC=5308.91
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    volatile.acidity:Type + Type:total.sulfur.dioxide

                           Df Deviance    AIC
+ density:Type              1   5281.0 5305.0
+ chlorides                 1   5283.6 5307.6
+ alcohol:Type              1   5283.8 5307.8
+ pH                        1   5284.1 5308.1
<none>                          5286.9 5308.9
+ free.sulfur.dioxide:Type  1   5285.6 5309.6
+ citric.acid               1   5285.8 5309.8
+ residual.sugar:Type       1   5286.2 5310.2
+ sulphates:Type            1   5286.3 5310.3
+ fixed.acidity             1   5286.8 5310.8

Step:  AIC=5305.04
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    volatile.acidity:Type + Type:total.sulfur.dioxide + density:Type

                           Df Deviance    AIC
+ pH                        1   5275.6 5301.6
+ residual.sugar:Type       1   5276.7 5302.7
+ chlorides                 1   5277.1 5303.1
<none>                          5281.0 5305.0
+ citric.acid               1   5279.1 5305.1
+ free.sulfur.dioxide:Type  1   5279.2 5305.2
+ fixed.acidity             1   5280.0 5306.0
+ alcohol:Type              1   5280.6 5306.6
+ sulphates:Type            1   5280.9 5306.9

Step:  AIC=5301.61
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    pH + volatile.acidity:Type + Type:total.sulfur.dioxide + 
    density:Type

                           Df Deviance    AIC
+ residual.sugar:Type       1   5270.3 5298.3
+ pH:Type                   1   5271.9 5299.9
+ chlorides                 1   5272.9 5300.9
<none>                          5275.6 5301.6
+ free.sulfur.dioxide:Type  1   5274.3 5302.3
+ fixed.acidity             1   5275.0 5303.0
+ citric.acid               1   5275.1 5303.1
+ sulphates:Type            1   5275.2 5303.2
+ alcohol:Type              1   5275.4 5303.4

Step:  AIC=5298.31
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    pH + volatile.acidity:Type + Type:total.sulfur.dioxide + 
    density:Type + residual.sugar:Type

                           Df Deviance    AIC
+ pH:Type                   1   5266.7 5296.7
+ chlorides                 1   5268.0 5298.0
<none>                          5270.3 5298.3
+ free.sulfur.dioxide:Type  1   5268.4 5298.4
+ fixed.acidity             1   5269.7 5299.7
+ citric.acid               1   5269.9 5299.9
+ sulphates:Type            1   5270.1 5300.1
+ alcohol:Type              1   5270.2 5300.2

Step:  AIC=5296.67
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    pH + volatile.acidity:Type + Type:total.sulfur.dioxide + 
    density:Type + residual.sugar:Type + Type:pH

                           Df Deviance    AIC
+ chlorides                 1   5263.4 5295.4
+ free.sulfur.dioxide:Type  1   5263.8 5295.8
<none>                          5266.7 5296.7
+ citric.acid               1   5265.9 5297.9
+ alcohol:Type              1   5266.4 5298.4
+ sulphates:Type            1   5266.6 5298.6
+ fixed.acidity             1   5266.6 5298.6

Step:  AIC=5295.44
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    pH + chlorides + volatile.acidity:Type + Type:total.sulfur.dioxide + 
    density:Type + residual.sugar:Type + Type:pH

                           Df Deviance    AIC
+ chlorides:Type            1   5259.3 5293.3
+ free.sulfur.dioxide:Type  1   5260.5 5294.5
<none>                          5263.4 5295.4
+ sulphates:Type            1   5262.7 5296.7
+ citric.acid               1   5263.0 5297.0
+ alcohol:Type              1   5263.2 5297.2
+ fixed.acidity             1   5263.4 5297.4

Step:  AIC=5293.31
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    pH + chlorides + volatile.acidity:Type + Type:total.sulfur.dioxide + 
    density:Type + residual.sugar:Type + Type:pH + Type:chlorides

                           Df Deviance    AIC
+ free.sulfur.dioxide:Type  1   5256.2 5292.2
<none>                          5259.3 5293.3
+ sulphates:Type            1   5257.9 5293.9
+ citric.acid               1   5258.9 5294.9
+ alcohol:Type              1   5259.3 5295.3
+ fixed.acidity             1   5259.3 5295.3

Step:  AIC=5292.16
cat_quality ~ alcohol + volatile.acidity + density + sulphates + 
    residual.sugar + Type + total.sulfur.dioxide + free.sulfur.dioxide + 
    pH + chlorides + volatile.acidity:Type + Type:total.sulfur.dioxide + 
    density:Type + residual.sugar:Type + Type:pH + Type:chlorides + 
    Type:free.sulfur.dioxide

                 Df Deviance    AIC
<none>                5256.2 5292.2
+ sulphates:Type  1   5254.7 5292.7
+ citric.acid     1   5255.9 5293.9
+ alcohol:Type    1   5256.1 5294.1
+ fixed.acidity   1   5256.2 5294.2

Call:  glm(formula = cat_quality ~ alcohol + volatile.acidity + density + 
    sulphates + residual.sugar + Type + total.sulfur.dioxide + 
    free.sulfur.dioxide + pH + chlorides + volatile.acidity:Type + 
    Type:total.sulfur.dioxide + density:Type + residual.sugar:Type + 
    Type:pH + Type:chlorides + Type:free.sulfur.dioxide, family = "binomial", 
    data = train)

Coefficients:
              (Intercept)                    alcohol  
                  9.68713                    0.84990  
         volatile.acidity                    density  
                 -2.84978                  -15.58322  
                sulphates             residual.sugar  
                  2.24908                    0.03117  
                     Type       total.sulfur.dioxide  
                195.20143                   -0.01898  
      free.sulfur.dioxide                         pH  
                  0.02478                   -0.60200  
                chlorides      volatile.acidity:Type  
                 -4.02470                   -3.50882  
Type:total.sulfur.dioxide               density:Type  
                  0.01756                 -201.96697  
      residual.sugar:Type                    Type:pH  
                  0.12808                    1.50862  
           Type:chlorides   Type:free.sulfur.dioxide  
                  5.10775                   -0.01620  

Degrees of Freedom: 5196 Total (i.e. Null);  5179 Residual
Null Deviance:      6833 
Residual Deviance: 5256     AIC: 5292

The forward step process dropped + sulphates:Type, fixed.acidity, alcohol:Type, and citric.acid By the hierarchical principle, the two non-interactive terms need to be added back because their have interaction terms are in the model.

 model1_int<-glm(formula = cat_quality ~ alcohol + volatile.acidity + density + 
    sulphates + residual.sugar +  Type + total.sulfur.dioxide + 
    free.sulfur.dioxide + pH + chlorides + volatile.acidity:Type + 
    Type:total.sulfur.dioxide + density:Type + residual.sugar:Type + 
    Type:pH + Type:chlorides + Type:free.sulfur.dioxide, family = "binomial", 
    data = train)
summary(model1_int)

Call:
glm(formula = cat_quality ~ alcohol + volatile.acidity + density + 
    sulphates + residual.sugar + Type + total.sulfur.dioxide + 
    free.sulfur.dioxide + pH + chlorides + volatile.acidity:Type + 
    Type:total.sulfur.dioxide + density:Type + residual.sugar:Type + 
    Type:pH + Type:chlorides + Type:free.sulfur.dioxide, family = "binomial", 
    data = train)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.2378  -0.8774   0.4148   0.8069   2.4950  

Coefficients:
                            Estimate Std. Error z value Pr(>|z|)    
(Intercept)                9.687e+00  4.539e+01   0.213 0.830982    
alcohol                    8.499e-01  5.665e-02  15.002  < 2e-16 ***
volatile.acidity          -2.850e+00  4.243e-01  -6.716 1.87e-11 ***
density                   -1.558e+01  4.495e+01  -0.347 0.728824    
sulphates                  2.249e+00  3.032e-01   7.418 1.19e-13 ***
residual.sugar             3.117e-02  5.020e-02   0.621 0.534702    
Type                       1.952e+02  5.575e+01   3.501 0.000463 ***
total.sulfur.dioxide      -1.897e-02  2.917e-03  -6.505 7.77e-11 ***
free.sulfur.dioxide        2.478e-02  8.602e-03   2.880 0.003971 ** 
pH                        -6.020e-01  4.860e-01  -1.239 0.215502    
chlorides                 -4.025e+00  1.527e+00  -2.636 0.008391 ** 
volatile.acidity:Type     -3.509e+00  6.200e-01  -5.659 1.52e-08 ***
Type:total.sulfur.dioxide  1.756e-02  3.200e-03   5.487 4.09e-08 ***
density:Type              -2.020e+02  5.584e+01  -3.617 0.000299 ***
residual.sugar:Type        1.281e-01  5.214e-02   2.456 0.014036 *  
Type:pH                    1.509e+00  5.610e-01   2.689 0.007159 ** 
Type:chlorides             5.108e+00  2.438e+00   2.095 0.036133 *  
Type:free.sulfur.dioxide  -1.620e-02  9.147e-03  -1.771 0.076642 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6833.2  on 5196  degrees of freedom
Residual deviance: 5256.2  on 5179  degrees of freedom
AIC: 5292.2

Number of Fisher Scoring iterations: 5

##evaluating model
model1_int_AIC_train <- model1_int$aic
##predicted quality for test data based on training data
preds<-predict(model1_int,newdata=test, type="response")
model1_int_error <- table(test$cat_quality, preds>0.7)
#Curves
evulation_summary_1int <- data.frame(
  attempt = 'model1_int',
  AIC = model1_int_AIC_train,
  PRESS = get_press(model1_int),
  'False positive' = round(model1_int_error[3]/(model1_int_error[1]+model1_int_error[3]),3),
  'False negative' = round(model1_int_error[2]/(model1_int_error[2]+model1_int_error[4]),3),
  'Error Rate' = round((model1_int_error[2]+model1_int_error[3])/(model1_int_error[1]+model1_int_error[2]+model1_int_error[3]+model1_int_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_1int)
evulation_summary

compare_models<-rbind(compare_models,evulation_summary_1int)
compare_models
NA
compare_models<-compare_models%>% 
  rename(
    Model = attempt
    )
library(data.table)
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
data.table 1.14.0 using 1 threads (see ?getDTthreads).  Latest news: r-datatable.com
**********
This installation of data.table has not detected OpenMP support. It should still work but in single-threaded mode.
This is a Mac. Please read https://mac.r-project.org/openmp/. Please engage with Apple and ask them for support. Check r-datatable.com for updates, and our Mac instructions here: https://github.com/Rdatatable/data.table/wiki/Installation. After several years of many reports of installation problems on Mac, it's time to gingerly point out that there have been no similar problems on Windows or Linux.
**********

Attaching package: ‘data.table’

The following objects are masked from ‘package:reshape2’:

    dcast, melt

The following objects are masked from ‘package:dplyr’:

    between, first, last

The following object is masked from ‘package:purrr’:

    transpose
library(dplyr)
library(formattable)
Registered S3 methods overwritten by 'htmltools':
  method               from         
  print.html           tools:rstudio
  print.shiny.tag      tools:rstudio
  print.shiny.tag.list tools:rstudio
Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio
library(tidyr)
customGreen0 = "#DeF7E9"

customGreen = "#71CA97"

customRed = "#ff7f7f"

formattable(compare_models,align =c("l","c", "c", "c", "c", "r"))

NA

Creating the ROC curves and AUC for the 3 new models.

# model1_Red
preds<-predict(model1_Red,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_Red")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
model1_Red_auc <- auc@y.values


# model1_White
preds<-predict(model1_White,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_White")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
model1_White_auc <- auc@y.values


# model1_int
preds<-predict(model1_int,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_int")
lines(x = c(0,1), y = c(0,1), col="red")


auc<-performance(rates, measure = "auc")
model1_int_auc <- auc@y.values

This is the one liners that run the tables and figures!


##create heat map Consolidated
ggplot(data = melted_cor_train, aes(x=Var1, y=Var2, fill=value)) + 
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+ 
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Consolidated (Both Red and White)')
##create heat map White
ggplot(data = melted_cor_train_white, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'White Wine')
##create heat map Red
ggplot(data = melted_cor_train_Red, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Red Wine')


ggplot(train_with_qual, mapping = aes(x=quality, fill=Type))+
  geom_histogram(binwidth=1, alpha=.4, position="identity", color="black")+
  geom_vline(aes(xintercept=5.5, color="red"),
             linetype="dashed")+
  scale_color_manual(name = "Cut Off", values = c("red"))+
  labs(x="Quality",
       y="Frequency",
       title="Distribution of Quality Rating by Wine Type")

This is the table for showing the evaluation for the first model

formattable(evulation_summary[1,])
summary(model1_Red)
summary(model1_White)
summary(model1_int)

Call:
glm(formula = cat_quality ~ alcohol + volatile.acidity + density + 
    sulphates + residual.sugar + Type + total.sulfur.dioxide + 
    free.sulfur.dioxide + pH + chlorides + volatile.acidity:Type + 
    Type:total.sulfur.dioxide + density:Type + residual.sugar:Type + 
    Type:pH + Type:chlorides + Type:free.sulfur.dioxide, family = "binomial", 
    data = train)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.2378  -0.8774   0.4148   0.8069   2.4950  

Coefficients:
                            Estimate Std. Error z value Pr(>|z|)    
(Intercept)                9.687e+00  4.539e+01   0.213 0.830982    
alcohol                    8.499e-01  5.665e-02  15.002  < 2e-16 ***
volatile.acidity          -2.850e+00  4.243e-01  -6.716 1.87e-11 ***
density                   -1.558e+01  4.495e+01  -0.347 0.728824    
sulphates                  2.249e+00  3.032e-01   7.418 1.19e-13 ***
residual.sugar             3.117e-02  5.020e-02   0.621 0.534702    
Type                       1.952e+02  5.575e+01   3.501 0.000463 ***
total.sulfur.dioxide      -1.897e-02  2.917e-03  -6.505 7.77e-11 ***
free.sulfur.dioxide        2.478e-02  8.602e-03   2.880 0.003971 ** 
pH                        -6.020e-01  4.860e-01  -1.239 0.215502    
chlorides                 -4.025e+00  1.527e+00  -2.636 0.008391 ** 
volatile.acidity:Type     -3.509e+00  6.200e-01  -5.659 1.52e-08 ***
Type:total.sulfur.dioxide  1.756e-02  3.200e-03   5.487 4.09e-08 ***
density:Type              -2.020e+02  5.584e+01  -3.617 0.000299 ***
residual.sugar:Type        1.281e-01  5.214e-02   2.456 0.014036 *  
Type:pH                    1.509e+00  5.610e-01   2.689 0.007159 ** 
Type:chlorides             5.108e+00  2.438e+00   2.095 0.036133 *  
Type:free.sulfur.dioxide  -1.620e-02  9.147e-03  -1.771 0.076642 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 6833.2  on 5196  degrees of freedom
Residual deviance: 5256.2  on 5179  degrees of freedom
AIC: 5292.2

Number of Fisher Scoring iterations: 5

Table right above the “Best Possible Model (Reduced_4)” section.

formattable(compare_models,align =c("l","c", "c", "c", "c", "r"))

This is the table for showing the best models (top five)

formattable(res.best.logistic$BestModels)

Add ROC for reduced_1, model1_Red, model1_White, model1_int


preds<-predict(reduced_1,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_1")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_1_auc <- auc@y.values
# model1_Red
preds<-predict(model1_Red,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_Red")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_Red_auc <- auc@y.values

# model1_White
preds<-predict(model1_White,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_White")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_White_auc <- auc@y.values

# model1_int
preds<-predict(model1_int,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_int")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_int_auc <- auc@y.values

This is the table for showing the best models (top five)

formattable(evulation_summary[2,])

This is the table for reduced_4 VIF.

formattable(data.frame(reg_4_VIF_test), align =c("l","r"))

This is the next VIF plot in the report

formattable(data.frame(reg_4_2_VIF_test), align =c("l","r"))

The table below that. It is the evaluation summary for reduced_4_2

formattable(evulation_summary[3,])

evaluation summary for the outlier/leverage/etc.

formattable(evulation_summary[4:7,])

add roc curves for these four.



## reduced_4
preds<-predict(reduced_4,newdata=test, type="response")
Error: variable 'Type' was fitted with type "numeric" but type "factor" was supplied

## reduced_4_2
preds<-predict(reduced_4_2,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_2")
lines(x = c(0,1), y = c(0,1), col="red")

auc4_2<-performance(rates, measure = "auc")
reduced_4_2_auc <- auc4_2@y.values

## reduced_4_3
preds<-predict(reduced_4_3,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_3")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_3_auc <- auc@y.values
## reduced_4_4_lev 
preds<-predict(reduced_4_4_lev,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_4_lev")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_4_lev_auc <- auc@y.values

## reduced_4_5_DDFFITS 
preds<-predict(reduced_4_5_DDFFITS,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_5_DDFFITS")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_5_DDFFITS_auc <- auc@y.values

## reduced_4_6_no_special 
preds<-predict(reduced_4_6_no_special,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_6_no_special")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_6_no_special_auc <- auc@y.values
AUC_summary <- data.frame('reduced_1'=reduced_1_auc,
                          'reduced_4'=reduced_4_auc,
                          'reduced_4_2'=reduced_4_2_auc,
                          'reduced_4_3'=reduced_4_3_auc,
                          'reduced_4_4_lev'=reduced_4_4_lev_auc,
                          'reduced_4_5_DDFFITS'=reduced_4_5_DDFFITS_auc,
                          'reduced_4_6_no_special'=reduced_4_6_no_special_auc)
colnames(AUC_summary) <- c('reduced_1','reduced_4','reduced_4_2','reduced_4_3','reduced_4_4_lev','reduced_4_5_DDFFITS','reduced_4_6_no_special')

AUC_summary

---
title: "R Notebook"
output: html_notebook
---



# pulling in DFs and Merging (still needed?)
```{r}
# #red wines
# Red_wine <- read.csv("wineQualityReds.csv", header=TRUE, sep = ",")
# Red_wine$Type <- 'Red'
# 
# #white wines
# White_wine <- read.csv("wineQualityWhites.csv", header=TRUE, sep = ",")
# White_wine$Type <- 'White'
# 
# ## consolidated
# Data <- rbind(Red_wine,White_wine)
# drops <- c("X")
# Data <- Data[ , !(names(Data) %in% drops)]
# Data
# 
# ##create final DF
# # write.csv(Data,"/Users/colinobrien/Desktop/repo/stats_6021/Stats_project_group_6/Data.csv", row.names = FALSE)
# # write.csv(Data,"/Users/colinobrien/Desktop/repo/stats_6021/Stats_project_group_6/Data", row.names = FALSE)
# ## both the Data and Data csv are the same. I know people prefer one format vs the other so I made both

```




```{r}
library(tidyverse)
# library(ROCR)
library(faraway)
library(dplyr)
library(ggplot2)
library(reshape2)
library(leaps)
# install.packages("bestglm")
library(bestglm)
# install.packages("performance")
# library(performance)
knitr::opts_chunk$set(echo = TRUE)



## Load Datasets
full_wines_final <- read.csv("Data_Final.csv", header = TRUE, stringsAsFactors=TRUE)
# Drop quality for simplicity
full_wines_binary_with_qual<-full_wines_final
full_wines_binary <- subset(full_wines_final, select = -c(quality))
## Convert to 0 and 1 for readability
full_wines_binary$cat_quality <- as.integer(full_wines_binary$cat_quality == "High")

set.seed(90210) ##for reproducibility
sample<-sample.int(nrow(full_wines_binary), floor(.80*nrow(full_wines_binary)), replace = F)
train<-full_wines_binary[sample, ] ##training data frame
rownames(train) <- c(1:5197)
test<-full_wines_binary[-sample, ] ##test data frame

## Just for a single boxplot
train_with_qual<-full_wines_binary_with_qual[sample,]
test_with_qual<-full_wines_binary_with_qual[-sample,]


train
```
# EDA


```{r}
# drops_cats <- c("Type")
# No_cat_train <- train[ , !(names(train) %in% drops_cats)]
# # No_Type

pairs(train, lower.panel = NULL)
```

```{r}
# Convert Type to binary to 0 and 1 for correlation
train$Type <- as.integer(train$Type == "White")
test$Type <- as.integer(test$Type == "White")
cor_train <- cor(train)
cor_train
```



```{r}
T_F_cor <- abs(cor_train)>.7
T_F_cor
```
```{r}
## create melted
melted_cor_train <- melt(cor_train)

##create heat map Consolidated
ggplot(data = melted_cor_train, aes(x=Var1, y=Var2, fill=value)) + 
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+ 
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Consolidated (Both Red and White)')




```

```{r}
## creating red and white
train_White <- filter(train, Type == 1)
train_Red <- filter(train, Type == 0)


## droping red/white columns
train_White_NoType <- subset(train_White, select = -c(Type))
train_Red_NoType <- subset(train_Red, select = -c(Type))

## creating correlations
cor_train_White_NoType <- cor(train_White_NoType)
cor_train_Red_NoType <- cor(train_Red_NoType)

## melting
melted_cor_train_white <- melt(cor_train_White_NoType)
melted_cor_train_Red <- melt(cor_train_Red_NoType)

##ploting

##create heat map White
ggplot(data = melted_cor_train_white, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'White Wine')

##create heat map Red
ggplot(data = melted_cor_train_Red, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Red Wine')

```

```{r}
ggplot(data = train, mapping = aes(x=Type)) + 
  geom_bar()
```

# Regression Testing

```{r}
## press formula (from class)
get_press <- function(model) {
  sum(((model$residuals)/ (1- (lm.influence(model)$hat)))^2)
}
```


```{r}
## first go
full<-glm(cat_quality~., family=binomial, data=train)
summary(full)
```
```{r}
## removed all insignificant
reduced_1<-glm(formula = cat_quality~volatile.acidity+residual.sugar+free.sulfur.dioxide+total.sulfur.dioxide+density+pH+sulphates+alcohol+Type, family=binomial, data=train)
summary(reduced_1)
```

```{r}
##evaluating model
Reduced1_AIC_train <- reduced_1$aic

##predicted quality for test data based on training data
preds<-predict(reduced_1,newdata=test, type="response")

reduced_1_error <- table(test$cat_quality, preds>0.5)

reduced_1_error

evulation_summary <- data.frame(
  attempt = 'reduced_1',
  AIC = Reduced1_AIC_train,
  PRESS = get_press(reduced_1),
  'False positive' = round(reduced_1_error[3]/(reduced_1_error[1]+reduced_1_error[3]),3),
  'False negative' = round(reduced_1_error[2]/(reduced_1_error[2]+reduced_1_error[4]),3),
  'Error Rate' = round((reduced_1_error[2]+reduced_1_error[3])/(reduced_1_error[1]+reduced_1_error[2]+reduced_1_error[3]+reduced_1_error[4]),3)
)
evulation_summary
```

## second model
## https://rstudio-pubs-static.s3.amazonaws.com/2897_9220b21cfc0c43a396ff9abf122bb351.html

```{r}
# install.packages("bestglm")
## Prepare data
train.for.best.logistic <- within(train, {
    y <- cat_quality 
})

## Reorder variables
train.for.best.logistic <-
    train.for.best.logistic[, c("fixed.acidity","volatile.acidity","citric.acid","residual.sugar","total.sulfur.dioxide","density","chlorides","free.sulfur.dioxide",'pH','sulphates','alcohol','Type',"y")]

## Perform
res.best.logistic <-
    bestglm(Xy = train.for.best.logistic,
            family = binomial,          # binomial family for logistic
            IC = "AIC",                 # Information criteria for
            method = "exhaustive")
```


```{r}
res.best.logistic$BestModels
summary(res.best.logistic$BestModel)
```
```{r}
reduced_4 <- res.best.logistic$BestModel
##evaluating model
Reduced4_AIC_train <- reduced_4$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4,newdata=test, type="response")

reduced_4_error <- table(test$cat_quality, preds>0.5)

evulation_summary_4 <- data.frame(
  attempt = 'reduced_4_error (all possible)',
  AIC = Reduced4_AIC_train,
  PRESS = get_press(reduced_4),
  'False positive' = round(reduced_4_error[3]/(reduced_4_error[1]+reduced_4_error[3]),3),
  'False negative' = round(reduced_4_error[2]/(reduced_4_error[2]+reduced_4_error[4]),3),
  'Error Rate' = round((reduced_4_error[2]+reduced_4_error[3])/(reduced_4_error[1]+reduced_4_error[2]+reduced_4_error[3]+reduced_4_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4)
# evulation_summary
```

```{r}
# data.frame(check_collinearity(reduced_4))










#come back and add df stuff
```

## in an effort to lower VIFs scores and correlation, I am removing fixed.acidity

```{r}
reduced_4_2<-glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train)
summary(reduced_4_2)
```
```{r}
##evaluating model
Reduced4_2_AIC_train <- reduced_4_2$aic
##predicted quality for test data based on training data
preds<-predict(reduced_4_2,newdata=test, type="response")
reduced_4_2_error <- table(test$cat_quality, preds>0.7)
#Curves
evulation_summary_4_2 <- data.frame(
  attempt = 'reduced_4_2_error (post VIF adjustments)',
  AIC = Reduced4_2_AIC_train,
  PRESS = get_press(reduced_4_2),
  'False positive' = round(reduced_4_2_error[3]/(reduced_4_2_error[1]+reduced_4_2_error[3]),3),
  'False negative' = round(reduced_4_2_error[2]/(reduced_4_2_error[2]+reduced_4_2_error[4]),3),
  'Error Rate' = round((reduced_4_2_error[2]+reduced_4_2_error[3])/(reduced_4_2_error[1]+reduced_4_2_error[2]+reduced_4_2_error[3]+reduced_4_2_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_2)
evulation_summary


```

## now looking at outliers (with "best possible")

```{r}
summary(reduced_4)

```


# Now looking into outliers/influence

```{r}
p <- 12
n <- 5197
```

### Cooks
```{r}
reduced_4_cook <-cooks.distance(reduced_4)
reduced_4_cook[reduced_4_cook>qf(0.5,p,n-p)]
```
### DFFITs

```{r}
##dffits
DFFITS<-dffits(reduced_4)
DDFFITS_influence <- DFFITS[abs(DFFITS)>2*sqrt(p/n)]
DDFFITS_influence
```
### DFBETAs
```{r}
DFBETAS<-dfbetas(reduced_4)
abs(DFBETAS)>2/sqrt(n)
```


### leverage
```{r}
##leverages
lev<-lm.influence(reduced_4)$hat
##identify high leverage points
leverages <- lev[lev>2*p/n]
leverages
```


### outlier

```{r}
reduced_4.res <- reduced_4$residuals
crit<-qt(1-0.05/(2*n), n-p-1)
outliers <- reduced_4.res[abs(reduced_4.res)>crit]
outliers
```




```{r}
## outliers removed
outliers_index <- attr(outliers, "names")
outliers_index <- as.numeric(outliers_index)
train_no_outliers <- train[-(outliers_index),]

#leverages removed
lererages_index <- attr(leverages, "names")
lererages_index <- as.numeric(lererages_index)
train_no_leverages <- train[-(lererages_index),]

# DDFFITS_influence
DDFFITS_index <- attr(DDFFITS_influence, "names")
DDFFITS_index <- as.numeric(DDFFITS_index)
train_no_DDFFITS <- train[-(DDFFITS_index),]

# all "non-normal" removed
all_special <- c(DDFFITS_index,lererages_index,outliers_index)
train_nothing_special <- train[-(all_special),]
train_nothing_special




```
```{r}
vif(train[c(2,3,4,7,8,6,9,10,11)])
```

```{r}
train_temp<-train
# as.factor(train_temp$Type)<-numeric(train_temp$Type)
#train_temp
# as.factor

train_temp$Type <- as.numeric(train_temp$Type)-1
train_temp$Type <- as.integer(train_temp$Type)
train_temp
```



## creating reduced 

```{r}
reduced_4_3 <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_no_outliers)

reduced_4_4_lev <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_no_leverages)

reduced_4_5_DDFFITS <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_no_DDFFITS)

reduced_4_6_no_special <- glm(cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type, family=binomial, data=train_nothing_special)
# summary(reduced_4_6_no_special)



```


```{r}
## checking colinearity / VIF scores
# reduced_4_3_col <- data.frame('reduced_4_3' = check_collinearity(reduced_4_3))
# reduced_4_3_col_VIF <- reduced_4_3_col[c('reduced_4_3.Term','reduced_4_3.VIF')]
# reduced_4_3_col_VIF
# 
# reduced_4_4_lev_col <- data.frame('reduced_4_4_lev' = check_collinearity(reduced_4_4_lev))
# reduced_4_4_lev_col_VIF <- reduced_4_4_lev_col[c('reduced_4_4_lev.Term','reduced_4_4_lev.VIF')]
# reduced_4_4_lev_col_VIF
# 
# 
# reduced_4_5_DDFFITS_col <- data.frame('reduced_4_5_DDFFITS' = check_collinearity(reduced_4_5_DDFFITS))
# reduced_4_5_DDFFITS_col_VIF <- reduced_4_5_DDFFITS_col[c('reduced_4_5_DDFFITS.Term','reduced_4_5_DDFFITS.VIF')]
# reduced_4_5_DDFFITS_col_VIF
# 
# reduced_4_6_no_special_col <- data.frame('reduced_4_6_no_special' = check_collinearity(reduced_4_6_no_special))
# reduced_4_6_no_special_col_VIF <- reduced_4_6_no_special_col[c('reduced_4_6_no_special.Term','reduced_4_6_no_special.VIF')]
# reduced_4_6_no_special_col_VIF
# 
# VIF_summary <- data.frame('0'=reduced_4_3_col_VIF['reduced_4_3.Term'],
#                           '1'=reduced_4_3_col_VIF['reduced_4_3.VIF'],
#                           '2'=reduced_4_4_lev_col_VIF['reduced_4_4_lev.VIF'],
#                           '3'=reduced_4_5_DDFFITS_col_VIF['reduced_4_5_DDFFITS.VIF'],
#                           '4'=reduced_4_6_no_special_col_VIF['reduced_4_6_no_special.VIF'])
# colnames(VIF_summary) <- c('Predictor Variable','4_3.VIF.Outliers','4_4_lev.VIF','4_5_DDFFITS.VIF','4_6_no_special.VIF')
# VIF_summary

## VIF for Outliers
### cat_quality~volatile.acidity+citric.acid+residual.sugar+total.sulfur.dioxide+density+free.sulfur.dioxide+pH+sulphates+alcohol+Type


#
reg_4_VIF_test <- vif(train_temp[c(1,2,3,4,7,8,6,9,10,11,12)])
reg_4_2_VIF_test <- vif(train_temp[c(2,3,4,7,8,6,9,10,11,12)])
outliers_VIF <- vif(train_no_outliers[c(2,3,4,7,8,6,9,10,11,12)])
leverage_VIF <- vif(train_no_leverages[c(2,3,4,7,8,6,9,10,11,12)])
DDFFITS_VIF <- vif(train_no_DDFFITS[c(2,3,4,7,8,6,9,10,11,12)])
nothing_special <- vif(train_nothing_special[c(2,3,4,7,8,6,9,10,11,12)])


reg_4_VIF_test

VIF_summary_test <- data.frame('best_possible_VIF (post)'=reg_4_2_VIF_test,
                               'outliers_VIF'=outliers_VIF,
                               'leverage_VIF'=leverage_VIF,
                               'DDFFITS_VIF'= DDFFITS_VIF,
                               'nothing_special'=nothing_special)
VIF_summary_test

```


```{r}
##evaluating model
Reduced4_3_AIC_train <- reduced_4_3$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_3,newdata=test, type="response")

reduced_4_3_error <- table(test$cat_quality, preds>0.6)

evulation_summary_4_3 <- data.frame(
  attempt = 'reduced_4_3_error_outliers',
  AIC = Reduced4_3_AIC_train,
  PRESS = get_press(reduced_4_3),
  'False positive' = round(reduced_4_3_error[3]/(reduced_4_3_error[1]+reduced_4_3_error[3]),3),
  'False negative' = round(reduced_4_3_error[2]/(reduced_4_3_error[2]+reduced_4_3_error[4]),3),
  'Error Rate' = round((reduced_4_3_error[2]+reduced_4_3_error[3])/(reduced_4_3_error[1]+reduced_4_3_error[2]+reduced_4_3_error[3]+reduced_4_3_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_3)
evulation_summary
```


```{r}
##evaluating model leverage
reduced_4_4_lev_AIC_train <- reduced_4_4_lev$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_4_lev,newdata=test, type="response")

reduced_4_4_lev_error <- table(test$cat_quality, preds>0.65)

evulation_summary_4_4_lev <- data.frame(
  attempt = 'reduced_4_4_lev_error',
  AIC = reduced_4_4_lev_AIC_train,
  PRESS = get_press(reduced_4_4_lev),
  'False positive' = round(reduced_4_4_lev_error[3]/(reduced_4_4_lev_error[1]+reduced_4_4_lev_error[3]),3),
  'False negative' = round(reduced_4_4_lev_error[2]/(reduced_4_4_lev_error[2]+reduced_4_4_lev_error[4]),3),
  'Error Rate' = round((reduced_4_4_lev_error[2]+reduced_4_4_lev_error[3])/(reduced_4_4_lev_error[1]+reduced_4_4_lev_error[2]+reduced_4_4_lev_error[3]+reduced_4_4_lev_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_4_lev)
evulation_summary
```



```{r}
##evaluating model DDFFITS
reduced_4_5_DDFFITS_AIC_train <- reduced_4_5_DDFFITS$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_5_DDFFITS,newdata=test, type="response")

reduced_4_5_DDFFITS_error <- table(test$cat_quality, preds>0.7)

evulation_summary_4_5_DDFFITS <- data.frame(
  attempt = 'reduced_4_5_DDFFITS_error',
  AIC = reduced_4_5_DDFFITS_AIC_train,
  PRESS = get_press(reduced_4_5_DDFFITS),
  'False positive' = round(reduced_4_5_DDFFITS_error[3]/(reduced_4_5_DDFFITS_error[1]+reduced_4_5_DDFFITS_error[3]),3),
  'False negative' = round(reduced_4_5_DDFFITS_error[2]/(reduced_4_5_DDFFITS_error[2]+reduced_4_5_DDFFITS_error[4]),3),
  'Error Rate' = round((reduced_4_5_DDFFITS_error[2]+reduced_4_5_DDFFITS_error[3])/(reduced_4_5_DDFFITS_error[1]+reduced_4_5_DDFFITS_error[2]+reduced_4_5_DDFFITS_error[3]+reduced_4_5_DDFFITS_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_5_DDFFITS)
evulation_summary
```

```{r}
##evaluating model DDFFITS
reduced_4_6_no_special_AIC_train <- reduced_4_6_no_special$aic

##predicted quality for test data based on training data
preds<-predict(reduced_4_6_no_special,newdata=test, type="response")

reduced_4_6_no_special_error <- table(test$cat_quality, preds>0.8)

evulation_summary_4_6_no_special <- data.frame(
  attempt = 'reduced_4_6_no_special_error',
  AIC = reduced_4_6_no_special_AIC_train,
  PRESS = get_press(reduced_4_6_no_special),
  'False positive' = round(reduced_4_6_no_special_error[3]/(reduced_4_6_no_special_error[1]+reduced_4_6_no_special_error[3]),3),
  'False negative' = round(reduced_4_6_no_special_error[2]/(reduced_4_6_no_special_error[2]+reduced_4_6_no_special_error[4]),3),
  'Error Rate' = round((reduced_4_6_no_special_error[2]+reduced_4_6_no_special_error[3])/(reduced_4_6_no_special_error[1]+reduced_4_6_no_special_error[2]+reduced_4_6_no_special_error[3]+reduced_4_6_no_special_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_4_6_no_special)
evulation_summary
```


## ROC Curves and AUC
```{r}
## reduced_1
# detach(package:performance, unload=TRUE)
## FYI the performance package causes ROC curves to not work
library(ROCR)



# reduced_1
preds<-predict(reduced_1,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_1")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_1_auc <- auc@y.values

## reduced_4
preds<-predict(reduced_4,newdata=test, type="response")
rates4<-prediction(preds, test$cat_quality)
roc_result<-performance(rates4,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4")
lines(x = c(0,1), y = c(0,1), col="red")

auc4<-performance(rates4, measure = "auc")
reduced_4_auc <- auc4@y.values

## reduced_4_2
preds<-predict(reduced_4_2,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_2")
lines(x = c(0,1), y = c(0,1), col="red")

auc4_2<-performance(rates, measure = "auc")
reduced_4_2_auc <- auc4_2@y.values

## reduced_4_3
preds<-predict(reduced_4_3,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_3")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_3_auc <- auc@y.values

## reduced_4_4_lev 
preds<-predict(reduced_4_4_lev,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_4_lev")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_4_lev_auc <- auc@y.values

## reduced_4_5_DDFFITS 
preds<-predict(reduced_4_5_DDFFITS,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_5_DDFFITS")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_5_DDFFITS_auc <- auc@y.values

## reduced_4_6_no_special 
preds<-predict(reduced_4_6_no_special,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_6_no_special")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_6_no_special_auc <- auc@y.values

AUC_summary <- data.frame('reduced_1'=reduced_1_auc,
                          'reduced_4'=reduced_4_auc,
                          'reduced_4_2'=reduced_4_2_auc,
                          'reduced_4_3'=reduced_4_3_auc,
                          'reduced_4_4_lev'=reduced_4_4_lev_auc,
                          'reduced_4_5_DDFFITS'=reduced_4_5_DDFFITS_auc,
                          'reduced_4_6_no_special'=reduced_4_6_no_special_auc)
colnames(AUC_summary) <- c('reduced_1','reduced_4','reduced_4_2','reduced_4_3','reduced_4_4_lev','reduced_4_5_DDFFITS','reduced_4_6_no_special')

AUC_summary
```





## Ryan's part starts here

### The goal is to make 3 models: One for just white, one for just red, and one with interaction terms with the type of wine. 

#### After that, the models will be trained on the filtered datasets and the resulting scores will be added to the evaluation summary.


## Red wine only model
```{r}
regfull_Red<-glm(cat_quality~., family="binomial", data=train_Red_NoType)
regnull_Red<-glm(cat_quality~1, family="binomial", data=train_Red_NoType)
step(regnull_Red, scope=list(lower=regnull_Red, upper=regfull_Red), direction="forward")

```


The model looks great after the foward selection! Time to test and add to the evaluation summary.
```{r}
model1_Red<-glm(formula = cat_quality ~ alcohol + volatile.acidity + total.sulfur.dioxide + 
    sulphates + free.sulfur.dioxide + chlorides, family = "binomial", 
    data = train_Red_NoType)

summary(model1_Red)


```

```{r}

##evaluating model
model1_Red_AIC_train <- model1_Red$aic
##predicted quality for test data based on training data
test_Red_NoType<-subset(test, Type == 0, select=-c(Type))
preds<-predict(model1_Red,newdata=test_Red_NoType, type="response")
model1_Red_error <- table(test_Red_NoType$cat_quality, preds>0.7)
#Curves
evulation_summary_1R <- data.frame(
  attempt = 'model1_Red',
  AIC = model1_Red_AIC_train,
  PRESS = get_press(model1_Red),
  'False positive' = round(model1_Red_error[3]/(model1_Red_error[1]+model1_Red_error[3]),3),
  'False negative' = round(model1_Red_error[2]/(model1_Red_error[2]+model1_Red_error[4]),3),
  'Error Rate' = round((model1_Red_error[2]+model1_Red_error[3])/(model1_Red_error[1]+model1_Red_error[2]+model1_Red_error[3]+model1_Red_error[4]),3)
)

compare_models<-rbind(evulation_summary[1,],evulation_summary_1R)
compare_models

evulation_summary <- rbind(evulation_summary,evulation_summary_1R)
evulation_summary

```
```{r}
# model1_Red
library(ROCR)
preds<-predict(model1_Red,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_Red")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_Red_auc <- auc@y.values

```

## White wine only model

```{r}
regfull_White<-glm(cat_quality~., family="binomial", data=train_White_NoType)
regnull_White<-glm(cat_quality~1,family="binomial", data=train_White_NoType)
step(regnull_White, scope=list(lower=regnull_White, upper=regfull_White), direction="forward")
```


The model looks good after the foward selection, but the predictor fixed.acidity can be removed. The density VIF is above ten, but jsut barely. For now, it will be left in. Time to test and add to the evaluation summary.
```{r}
model1_White<-glm(formula = cat_quality ~ alcohol + volatile.acidity + residual.sugar + 
    fixed.acidity + sulphates + free.sulfur.dioxide + density + 
    pH, family = "binomial", data = train_White_NoType)


summary(model1_White)


model1_White<-glm(formula = cat_quality ~ alcohol + volatile.acidity + residual.sugar + sulphates + free.sulfur.dioxide + density + 
    pH, family = "binomial", data = train_White_NoType)

summary(model1_White)


```


```{r}

##evaluating model
model1_White_AIC_train <- model1_White$aic
##predicted quality for test data based on training data
test_White_NoType<-subset(test, Type == 1, select=-c(Type))
preds<-predict(model1_White,newdata=test_White_NoType, type="response")
model1_White_error <- table(test_White_NoType$cat_quality, preds>0.7)
#Curves
evulation_summary_1W <- data.frame(
  attempt = 'model1_White',
  AIC = model1_White_AIC_train,
  PRESS = get_press(model1_White),
  'False positive' = round(model1_White_error[3]/(model1_White_error[1]+model1_White_error[3]),3),
  'False negative' = round(model1_White_error[2]/(model1_White_error[2]+model1_White_error[4]),3),
  'Error Rate' = round((model1_White_error[2]+model1_White_error[3])/(model1_White_error[1]+model1_White_error[2]+model1_White_error[3]+model1_White_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_1W)
evulation_summary


compare_models<-rbind(compare_models,evulation_summary_1W)
compare_models

```



## The model with interaction terms

```{r}
regfull_int<-glm(cat_quality~.*Type, family="binomial", data=train)
regnull_int<-glm(cat_quality~1,family="binomial", data=train)
step(regnull_int, scope=list(lower=regnull_int, upper=regfull_int), direction="forward")
```


The forward step process dropped + sulphates:Type, fixed.acidity, alcohol:Type, and citric.acid  By the hierarchical principle, the two non-interactive terms need to be added back because their have interaction terms are in the model.
```{r}
 model1_int<-glm(formula = cat_quality ~ alcohol + volatile.acidity + density + 
    sulphates + residual.sugar +  Type + total.sulfur.dioxide + 
    free.sulfur.dioxide + pH + chlorides + volatile.acidity:Type + 
    Type:total.sulfur.dioxide + density:Type + residual.sugar:Type + 
    Type:pH + Type:chlorides + Type:free.sulfur.dioxide, family = "binomial", 
    data = train)
summary(model1_int)

```


```{r}

##evaluating model
model1_int_AIC_train <- model1_int$aic
##predicted quality for test data based on training data
preds<-predict(model1_int,newdata=test, type="response")
model1_int_error <- table(test$cat_quality, preds>0.7)
#Curves
evulation_summary_1int <- data.frame(
  attempt = 'model1_int',
  AIC = model1_int_AIC_train,
  PRESS = get_press(model1_int),
  'False positive' = round(model1_int_error[3]/(model1_int_error[1]+model1_int_error[3]),3),
  'False negative' = round(model1_int_error[2]/(model1_int_error[2]+model1_int_error[4]),3),
  'Error Rate' = round((model1_int_error[2]+model1_int_error[3])/(model1_int_error[1]+model1_int_error[2]+model1_int_error[3]+model1_int_error[4]),3)
)

evulation_summary <- rbind(evulation_summary,evulation_summary_1int)
evulation_summary

compare_models<-rbind(compare_models,evulation_summary_1int)
compare_models

```

```{r}
compare_models<-compare_models%>% 
  rename(
    Model = attempt
    )

```


```{r}
library(data.table)
library(dplyr)
library(formattable)
library(tidyr)
customGreen0 = "#DeF7E9"

customGreen = "#71CA97"

customRed = "#ff7f7f"

```













Creating the ROC curves and AUC for the 3 new models.
```{r}
# model1_Red
preds<-predict(model1_Red,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_Red")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_Red_auc <- auc@y.values


# model1_White
preds<-predict(model1_White,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_White")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_White_auc <- auc@y.values


# model1_int
preds<-predict(model1_int,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_int")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_int_auc <- auc@y.values
```
























## This is the one liners that run the tables and figures!





```{r}

##create heat map Consolidated
ggplot(data = melted_cor_train, aes(x=Var1, y=Var2, fill=value)) + 
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+ 
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Consolidated (Both Red and White)')

```

```{r}
##create heat map White
ggplot(data = melted_cor_train_white, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'White Wine')

```

```{r}
##create heat map Red
ggplot(data = melted_cor_train_Red, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile(color = "white")+
  scale_fill_gradient2(low = "blue", high = "red", mid = "white", midpoint = 0, limit = c(-1,1), space = "Lab", name="Pearson\nCorrelation") +
  theme_minimal()+
  theme(axis.text.x = element_text(angle = 45, vjust = 1, size = 12, hjust = 1))+
  coord_fixed()+
  labs(title = 'Red Wine')

```





```{r}


ggplot(train_with_qual, mapping = aes(x=quality, fill=Type))+
  geom_histogram(binwidth=1, alpha=.4, position="identity", color="black")+
  geom_vline(aes(xintercept=5.5, color="red"),
             linetype="dashed")+
  scale_color_manual(name = "Cut Off", values = c("red"))+
  labs(x="Quality",
       y="Frequency",
       title="Distribution of Quality Rating by Wine Type")
```



This is the table for showing the evaluation for the first model
```{r}
formattable(evulation_summary[1,])
```



```{r}
summary(model1_Red)
```

```{r}
summary(model1_White)
```


```{r}
summary(model1_int)
```




Table right above the "Best Possible Model (Reduced_4)" section.
```{r}
formattable(compare_models,align =c("l","c", "c", "c", "c", "r"))

```




This is the table for showing the best models (top five)
```{r}
formattable(res.best.logistic$BestModels)
```


Add ROC for reduced_1, model1_Red, model1_White, model1_int

```{r}

preds<-predict(reduced_1,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_1")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_1_auc <- auc@y.values

```


```{r}
# model1_Red
preds<-predict(model1_Red,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_Red")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_Red_auc <- auc@y.values

```

```{r}

# model1_White
preds<-predict(model1_White,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_White")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_White_auc <- auc@y.values

```

```{r}

# model1_int
preds<-predict(model1_int,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for model1_int")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
model1_int_auc <- auc@y.values
```


This is the table for showing the best models (top five)
```{r}
formattable(evulation_summary[2,])
```


This is the table for reduced_4 VIF.
```{r}
formattable(data.frame(reg_4_VIF_test), align =c("l","r"))
```

This is the next VIF plot in the report
```{r}
formattable(data.frame(reg_4_2_VIF_test), align =c("l","r"))
```


The table below that. It is the evaluation summary for reduced_4_2
```{r}
formattable(evulation_summary[3,])
```


evaluation summary for the outlier/leverage/etc.
```{r}
formattable(evulation_summary[4:7,])
```



add roc curves for these four.

```{r}


## reduced_4
preds<-predict(reduced_4,newdata=test, type="response")
rates4<-prediction(preds, test$cat_quality)
roc_result<-performance(rates4,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4")
lines(x = c(0,1), y = c(0,1), col="red")

auc4<-performance(rates4, measure = "auc")
reduced_4_auc <- auc4@y.values

```

```{r}

## reduced_4_2
preds<-predict(reduced_4_2,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_2")
lines(x = c(0,1), y = c(0,1), col="red")

auc4_2<-performance(rates, measure = "auc")
reduced_4_2_auc <- auc4_2@y.values

```


```{r}

## reduced_4_3
preds<-predict(reduced_4_3,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_3")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_3_auc <- auc@y.values


```


```{r}
## reduced_4_4_lev 
preds<-predict(reduced_4_4_lev,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_4_lev")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_4_lev_auc <- auc@y.values

```

```{r}

## reduced_4_5_DDFFITS 
preds<-predict(reduced_4_5_DDFFITS,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_5_DDFFITS")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_5_DDFFITS_auc <- auc@y.values

```




```{r}

## reduced_4_6_no_special 
preds<-predict(reduced_4_6_no_special,newdata=test, type="response")
rates<-prediction(preds, test$cat_quality)
roc_result<-performance(rates,measure="tpr", x.measure="fpr")
plot(roc_result, main="ROC Curve for reduced_4_6_no_special")
lines(x = c(0,1), y = c(0,1), col="red")

auc<-performance(rates, measure = "auc")
reduced_4_6_no_special_auc <- auc@y.values

```

```{r}
AUC_summary <- data.frame('reduced_1'=reduced_1_auc,
                          'reduced_4'=reduced_4_auc,
                          'reduced_4_2'=reduced_4_2_auc,
                          'reduced_4_3'=reduced_4_3_auc,
                          'reduced_4_4_lev'=reduced_4_4_lev_auc,
                          'reduced_4_5_DDFFITS'=reduced_4_5_DDFFITS_auc,
                          'reduced_4_6_no_special'=reduced_4_6_no_special_auc)
colnames(AUC_summary) <- c('reduced_1','reduced_4','reduced_4_2','reduced_4_3','reduced_4_4_lev','reduced_4_5_DDFFITS','reduced_4_6_no_special')

AUC_summary
```





#


